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Sum of n terms of AP - Arithmetic Progressions (AP) Video Lecture - Class
FAQs on Sum of n terms of AP - Arithmetic Progressions (AP)
| 1. What is an arithmetic progression (AP)? |  |
Ans. An arithmetic progression (AP) is a sequence of numbers in which the difference between any two consecutive terms is constant. For example, 2, 5, 8, 11, 14 is an AP with a common difference of 3.
| 2. How do you find the sum of n terms of an AP? | |
Ans. The sum of the first n terms of an arithmetic progression (AP) can be calculated using the formula: Sn = (n/2)(2a + (n-1)d), where Sn represents the sum of the n terms, a is the first term, and d is the common difference.
| 3. Can the sum of n terms of an AP be negative? | |
Ans. Yes, the sum of n terms of an arithmetic progression (AP) can be negative if the terms in the AP alternate between positive and negative values. In such cases, the sum can be negative depending on the values of the terms and the number of terms.
| 4. Is it necessary for an AP to have a positive common difference? | |
Ans. No, an arithmetic progression (AP) can have a negative common difference as well. The common difference can be any real number, positive or negative. It determines the pattern of the sequence, whether it increases or decreases.
| 5. Can the sum of n terms of an AP be a decimal or fraction? | |
Ans. Yes, the sum of n terms of an arithmetic progression (AP) can be a decimal or fraction. The sum is not limited to whole numbers and can take any real value depending on the sequence of terms and the number of terms.
Text Transcript from Video
hello friends this video on arithmetic
progressions part 11 is brought to you
by exam viacom no more fear from exam
they for watching this video please make
sure that you have watched part 1 to
part 10 let's trick from example where
we have to find Eevee here a is equal to
5 T is equal to 3 in a.m. is equal to 50
we have to find n NSF very simple a n is
equal to a plus n minus 1 be correct
because we have a n is given C to find
some we should have a N and B so here
we'll find n and then we'll finest so a
n is 50 is equal to a is I plus n minus
1 imagery n minus 1 is nothing but 50
minus 5 by 3 45 by 3 that is 30 so n is
good to succeed I have got the value of
n I have got the value of n so I can
find us in as there is nothing n by 2
the way plus and minus 1 D correct same
formula and is 16 16 by 2 into a is 5
plus n minus 1 is 15 now because n is 16
into B is 3 correct so this I get 8 into
5 10 10 plus 53 45 that is 55 into 8 and
that is nothing but 4 40
and that is minus T very simple what I
have done I had this value of en I got
the value of n because to find SN I need
nd any and also the question also asked
me to find a wide open
I got develop n to be 60 n SN to be poor
for me it was take home for example a 7
e 13 is 35 we defined DN s 3x 30s 30 so
a 13 is nothing bad a plus 20
all right and that is 35 given here over
given 7 plus is 7 7 plus 27 to 35 see a
13 is given that is 35
right a is given to the seven define D
so D is nothing word 35 minus 7 by 12
that is 28 by 12 and that is only word 7
by 3 so I have got the Vedad one side
the value of D I can find is 30 as 13 is
nothing but n by 2 into 2 8 plus n minus
1 D correct or I can use this formula
and white will do it plus e 13 last term
and instead of 13 here obviously 13 by 2
into is 7 and a third is 35 this has
nothing but 13 by 2 into 14 13 by 2 in
departing 42 by 2 is 21 so 13 into 21
that is 750 is nice very simple see a 13
was given and a 13 is a plus 20 a was
given on the value of D D was now they
asked us to find some of 13 dumps we can
use the formula n by 2 into 8 plus a 13
but because a 13 is L and we know that
some of them is nothing but n by 2 into
B implicit we can use this formula also
but this will be longer since we only
know and a and a 13 we can just try to
use the bomb and way hotter and the
question says how many terms of AP must
be taken to get some of 636 so here also
if you see the first thing log service a
is 9 d is 70 minus 9 is 25 minus 17
today is going to be correct the
question says s set is equal to 6 36 we
have to find them alone apply the
formula SN is going to n by 2 into 2 8
plus n minus 1 T correct or 6 36
- n is going to we don't know and by 2
into 2 a is 9 + n - 1 DZ this is what we
have got all right
- like in cancer here using controller
so I will get 9 n+ who else by -4 n is
equal to 36 + ordinary equation n into 9
n + n - 1 or I get Oh L square plus 5n
minus 6 3600 this is a quadratic
equation we have already learned how to
solve the quadratic equation then
factorize this the factorizes this
becomes over N square plus 53 n minus 48
n minus 6 36 it is factorize it because
mine + 53-48 is going to file and 53
into 48 minus 48 is going to you
multiply this 4 into 6 36 now I take n
common this becomes 4n + 53 and this
becomes minus 48 what 48 big - - well
common why because I get 48 here where
in the forum correct is producer so I
will get n is going to be 12 or n is
equal to minus 53 wife oh mm-
not possible author its factor one
possible so n is relative in advance so
12 term to be taken so that sum is 6 36
very simple what we have now be head of
a we have devfs in we have to find the
value of n we use this formula we got a
cadre equation its ordinate to get
develop n is equal to 2 let's take one
more example the first term of AP is 5
the last term of AP is 45 and the 7 spot
find the number of terms and foundations
that is a
five L is equal to 45 right
SN is equal to 400 we have to find MND
we know that SN is nothing bad and white
2 into a plus a correct or 400 is
nothing where and by 2 into a 5 plus 40
correct or n is nothing but 400 into by
spot to fight for it by 50 current so n
is nothing but 60 you have or develop in
n is 60 right now I divide the value of
D so a 16 is equal to 45 correct because
L is 45 and that is nothing but a plus n
minus 1 T that is 15 including correct
or I can say 45 is equal to a is 5 plus
15 D or D is nothing but 45 minus 5 by
15 that is 40 by 50 or again saying this
is 8 5 is 40 + 3 8 by 3 so D is equal to
8 by 3 and n is equal to 60 is fancy
very super just direct application of
formula automatic is very very simple
just you have to understand the question
and directly apply the formula and get
up here what we have done SN is going to
n by 2 into a plus L the right
application of formula we got n is equal
to 16 since n is equal to 16 a 16 is
going to L last term and so we got these
buttons if I let us take one more
example find the sum of those 22 terms
of AP for which D is equal to 7 and 20
second term is 49 that is d is equal to
7 and a 22 is between 140 correct so you
can say that a 22 is nothing but a plus
21 d or 149
is equal to 8 plus 2187 or we can say a
is nothing worth 149 - 25 - 7 7 holding
current or a is good we have a right we
have N and we have ellos because a 22 0
we can find to some very simple as well
as nothing word and wait to include
lesson and it's 22 when you go by 2 is
to be in this form l is 149 given
because a 22 is 49 there is nothing but
11 in 151 that is 1 6 6 4 and that is my
answer so somehow first 22 terms is 161
let is input direct application of we'll
take one more example so that a 1 a 2 a
n for any a B where n is defined as n is
equal to 3 plus 4n or here is going to 9
- 5 m they are both the video to show
that correct so let us take first one so
in first case even is nothing but 3 plus
4 is 7 a 2 is nothing but 3 plus going
into that is clever and a 3 is nothing
word 3 plus 4 into G that is 2a plus 3
simply if you see the difference if you
see the CD CD is nothing but 7 11 15 on
this small the difference is for
constant so we can see that this is a B
that means this is different because the
difference is for constant these four in
a is 7 so we can see them this
similarly for the next one a 1 is
nothing but 9 minus 5 that is 4 a 2 is
nothing but 9 minus 5 into 2 that is
minus 1 in 3 is nothing but 9 minus 5
into 3 that is minus 6 so if you see
here the series comes out to be 4 minus
1 minus 6 the reference is minus 5 right
so we can see that this is also
very simple you just fine first two
terms and then if you show that that is
the name in the sum of first n term of
ApS or n minus n square
what is the first what is the sum of
first two dumb what is second term and
separately third 10 then the question C
is then the first SN is equal to 4 n
minus is 5 correct so I can see that s 1
is nothing but 4 into 1 minus 1 square
that is 3 and s 1 is nothing but a we
know this C in term which has only one
term first term somewhat first term is
same so this one is going to be one a so
or a is equal to this is my first
equation s 2 is nothing but 4 a 2 2
minus 2 square that is 8 minus 4 that is
4 correct so if I am talking about s 2
if I have done a a plus D a plus dou T
of this form s 2 is nothing but a plus a
plus D correct first term and second
term some correct and this is nothing
but 4 or 2 a plus D is going for a 3 B
already so we can say it D is nothing
but 4 minus 2 a it is 2 into 3 that is 4
minus 6 that is minus 2 so I have got B
is equal to minus 2 he is the 2 minus 2
by God a is equal to 3 and D is equal to
minus 2 or this a B I have a nd I am
everything correct why hands formula a n
is going to a plus n minus 1 T correct a
is nothing but 3 plus n minus 1 and D
have evil - to correct this comes out to
be 3 minus 3 n plus 2 that is 5 minus
yes to the national hi my next one so
ans pie minus 2 this is zero for my god
now I have to find the first term or
third them to find third term a 3 is
nothing but PI minus instead of ni
divided 3 this becomes 5 minus 6 that is
minus 1 if I am to find tens down 10th
term is nothing but pi minus 2 into 10
issue of n I am just putting 10 I get 5
minutes went against innocent people so
this is my third term this is my tenth
term and the first term is already very
simple you have got SN to get the first
term a is nothing but s 1 we got a story
then we found s 2 you say s 2 s 2 is
nothing but a plus C plus D you can see
here s to nothing but you add these two
terms right you already have the value
of a we got the value of DB minus T we
have a we have D we have everything you
can use the formula n is equal to a plus
n minus 1 D correct we have the value of
a and D pair putted we got general
formula n is good nothing but 5 minutes
to 4 a 3 B a used n is equal to 3 to n
minus 1 for 18 you got n is going to 10
again - next it thank you
visit exam viacom to watch
free education videos try free online
tests get the best quality study
materials study from the best tutors and
mentors and much more thanks on screen
progressions part 11 is brought to you
by exam viacom no more fear from exam
they for watching this video please make
sure that you have watched part 1 to
part 10 let's trick from example where
we have to find Eevee here a is equal to
5 T is equal to 3 in a.m. is equal to 50
we have to find n NSF very simple a n is
equal to a plus n minus 1 be correct
because we have a n is given C to find
some we should have a N and B so here
we'll find n and then we'll finest so a
n is 50 is equal to a is I plus n minus
1 imagery n minus 1 is nothing but 50
minus 5 by 3 45 by 3 that is 30 so n is
good to succeed I have got the value of
n I have got the value of n so I can
find us in as there is nothing n by 2
the way plus and minus 1 D correct same
formula and is 16 16 by 2 into a is 5
plus n minus 1 is 15 now because n is 16
into B is 3 correct so this I get 8 into
5 10 10 plus 53 45 that is 55 into 8 and
that is nothing but 4 40
and that is minus T very simple what I
have done I had this value of en I got
the value of n because to find SN I need
nd any and also the question also asked
me to find a wide open
I got develop n to be 60 n SN to be poor
for me it was take home for example a 7
e 13 is 35 we defined DN s 3x 30s 30 so
a 13 is nothing bad a plus 20
all right and that is 35 given here over
given 7 plus is 7 7 plus 27 to 35 see a
13 is given that is 35
right a is given to the seven define D
so D is nothing word 35 minus 7 by 12
that is 28 by 12 and that is only word 7
by 3 so I have got the Vedad one side
the value of D I can find is 30 as 13 is
nothing but n by 2 into 2 8 plus n minus
1 D correct or I can use this formula
and white will do it plus e 13 last term
and instead of 13 here obviously 13 by 2
into is 7 and a third is 35 this has
nothing but 13 by 2 into 14 13 by 2 in
departing 42 by 2 is 21 so 13 into 21
that is 750 is nice very simple see a 13
was given and a 13 is a plus 20 a was
given on the value of D D was now they
asked us to find some of 13 dumps we can
use the formula n by 2 into 8 plus a 13
but because a 13 is L and we know that
some of them is nothing but n by 2 into
B implicit we can use this formula also
but this will be longer since we only
know and a and a 13 we can just try to
use the bomb and way hotter and the
question says how many terms of AP must
be taken to get some of 636 so here also
if you see the first thing log service a
is 9 d is 70 minus 9 is 25 minus 17
today is going to be correct the
question says s set is equal to 6 36 we
have to find them alone apply the
formula SN is going to n by 2 into 2 8
plus n minus 1 T correct or 6 36
- n is going to we don't know and by 2
into 2 a is 9 + n - 1 DZ this is what we
have got all right
- like in cancer here using controller
so I will get 9 n+ who else by -4 n is
equal to 36 + ordinary equation n into 9
n + n - 1 or I get Oh L square plus 5n
minus 6 3600 this is a quadratic
equation we have already learned how to
solve the quadratic equation then
factorize this the factorizes this
becomes over N square plus 53 n minus 48
n minus 6 36 it is factorize it because
mine + 53-48 is going to file and 53
into 48 minus 48 is going to you
multiply this 4 into 6 36 now I take n
common this becomes 4n + 53 and this
becomes minus 48 what 48 big - - well
common why because I get 48 here where
in the forum correct is producer so I
will get n is going to be 12 or n is
equal to minus 53 wife oh mm-
not possible author its factor one
possible so n is relative in advance so
12 term to be taken so that sum is 6 36
very simple what we have now be head of
a we have devfs in we have to find the
value of n we use this formula we got a
cadre equation its ordinate to get
develop n is equal to 2 let's take one
more example the first term of AP is 5
the last term of AP is 45 and the 7 spot
find the number of terms and foundations
that is a
five L is equal to 45 right
SN is equal to 400 we have to find MND
we know that SN is nothing bad and white
2 into a plus a correct or 400 is
nothing where and by 2 into a 5 plus 40
correct or n is nothing but 400 into by
spot to fight for it by 50 current so n
is nothing but 60 you have or develop in
n is 60 right now I divide the value of
D so a 16 is equal to 45 correct because
L is 45 and that is nothing but a plus n
minus 1 T that is 15 including correct
or I can say 45 is equal to a is 5 plus
15 D or D is nothing but 45 minus 5 by
15 that is 40 by 50 or again saying this
is 8 5 is 40 + 3 8 by 3 so D is equal to
8 by 3 and n is equal to 60 is fancy
very super just direct application of
formula automatic is very very simple
just you have to understand the question
and directly apply the formula and get
up here what we have done SN is going to
n by 2 into a plus L the right
application of formula we got n is equal
to 16 since n is equal to 16 a 16 is
going to L last term and so we got these
buttons if I let us take one more
example find the sum of those 22 terms
of AP for which D is equal to 7 and 20
second term is 49 that is d is equal to
7 and a 22 is between 140 correct so you
can say that a 22 is nothing but a plus
21 d or 149
is equal to 8 plus 2187 or we can say a
is nothing worth 149 - 25 - 7 7 holding
current or a is good we have a right we
have N and we have ellos because a 22 0
we can find to some very simple as well
as nothing word and wait to include
lesson and it's 22 when you go by 2 is
to be in this form l is 149 given
because a 22 is 49 there is nothing but
11 in 151 that is 1 6 6 4 and that is my
answer so somehow first 22 terms is 161
let is input direct application of we'll
take one more example so that a 1 a 2 a
n for any a B where n is defined as n is
equal to 3 plus 4n or here is going to 9
- 5 m they are both the video to show
that correct so let us take first one so
in first case even is nothing but 3 plus
4 is 7 a 2 is nothing but 3 plus going
into that is clever and a 3 is nothing
word 3 plus 4 into G that is 2a plus 3
simply if you see the difference if you
see the CD CD is nothing but 7 11 15 on
this small the difference is for
constant so we can see that this is a B
that means this is different because the
difference is for constant these four in
a is 7 so we can see them this
similarly for the next one a 1 is
nothing but 9 minus 5 that is 4 a 2 is
nothing but 9 minus 5 into 2 that is
minus 1 in 3 is nothing but 9 minus 5
into 3 that is minus 6 so if you see
here the series comes out to be 4 minus
1 minus 6 the reference is minus 5 right
so we can see that this is also
very simple you just fine first two
terms and then if you show that that is
the name in the sum of first n term of
ApS or n minus n square
what is the first what is the sum of
first two dumb what is second term and
separately third 10 then the question C
is then the first SN is equal to 4 n
minus is 5 correct so I can see that s 1
is nothing but 4 into 1 minus 1 square
that is 3 and s 1 is nothing but a we
know this C in term which has only one
term first term somewhat first term is
same so this one is going to be one a so
or a is equal to this is my first
equation s 2 is nothing but 4 a 2 2
minus 2 square that is 8 minus 4 that is
4 correct so if I am talking about s 2
if I have done a a plus D a plus dou T
of this form s 2 is nothing but a plus a
plus D correct first term and second
term some correct and this is nothing
but 4 or 2 a plus D is going for a 3 B
already so we can say it D is nothing
but 4 minus 2 a it is 2 into 3 that is 4
minus 6 that is minus 2 so I have got B
is equal to minus 2 he is the 2 minus 2
by God a is equal to 3 and D is equal to
minus 2 or this a B I have a nd I am
everything correct why hands formula a n
is going to a plus n minus 1 T correct a
is nothing but 3 plus n minus 1 and D
have evil - to correct this comes out to
be 3 minus 3 n plus 2 that is 5 minus
yes to the national hi my next one so
ans pie minus 2 this is zero for my god
now I have to find the first term or
third them to find third term a 3 is
nothing but PI minus instead of ni
divided 3 this becomes 5 minus 6 that is
minus 1 if I am to find tens down 10th
term is nothing but pi minus 2 into 10
issue of n I am just putting 10 I get 5
minutes went against innocent people so
this is my third term this is my tenth
term and the first term is already very
simple you have got SN to get the first
term a is nothing but s 1 we got a story
then we found s 2 you say s 2 s 2 is
nothing but a plus C plus D you can see
here s to nothing but you add these two
terms right you already have the value
of a we got the value of DB minus T we
have a we have D we have everything you
can use the formula n is equal to a plus
n minus 1 D correct we have the value of
a and D pair putted we got general
formula n is good nothing but 5 minutes
to 4 a 3 B a used n is equal to 3 to n
minus 1 for 18 you got n is going to 10
again - next it thank you
visit exam viacom to watch
free education videos try free online
tests get the best quality study
materials study from the best tutors and
mentors and much more thanks on screen
About this Video
Apr 20, 2026 Last updated
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