Class 11 Exam > Class 11 Videos > Examples AP Arithmetic Progression-1(Part - 6)- Sequences and Series, Mathematics, Class 11
Examples AP Arithmetic Progression-1(Part - 6)- Sequences and Series, Mathematics, Class 11 Video Lecture
FAQs on Examples AP Arithmetic Progression-1(Part - 6)- Sequences and Series, Mathematics, Class 11 Video Lecture
| 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 arithmetic progression with a common difference of 3.
| 2. How can I find the nth term of an arithmetic progression? | |
Ans. To find the nth term of an arithmetic progression, you can use the formula: nth term = first term + (n-1) * common difference. For example, if the first term is 3 and the common difference is 2, the nth term can be calculated using the formula nth term = 3 + (n-1) * 2.
| 3. How do I determine if a given sequence is an arithmetic progression? | |
Ans. To determine if a given sequence is an arithmetic progression, check if the difference between any two consecutive terms is constant. If the difference remains the same throughout the sequence, then it is an arithmetic progression. If the difference varies, it is not an arithmetic progression.
| 4. Can the common difference in an arithmetic progression be negative? | |
Ans. Yes, the common difference in an arithmetic progression can be negative. The common difference represents the amount by which each term increases or decreases, and it can be positive or negative depending on the pattern of the sequence.
| 5. How can I find the sum of an arithmetic series? | |
Ans. The sum of an arithmetic series can be found using the formula: sum = (n/2) * (first term + last term), where n is the number of terms in the series. Alternatively, you can use the formula: sum = (n/2) * (2a + (n-1)d), where a is the first term and d is the common difference.
Text Transcript from Video
hello friends this video sequence and
series part 6 is brought to you by exam
fear calm no more fear from exam before
watching this video please make sure
that you have washed video part 1 - Part
5 examples of soft thumbs so we had to
want to find the terms of EB we are told
to find the term some of the terms of
this sequence but we are not told where
there is an EP or chip first we need to
find whether VP or not so the sequence
is 2 4 6 7 e 10 the difference between
24 X - 4 into 6 is 2 6 7 is 1 7 8 is 1 8
in the list you see the difference is
not constant here it is 1 here it is 2
that means it is not an sin it is not an
AP and we have not learned anything else
till not now as of now we cannot solve
this question whether it is not an AP so
we can't serve because we know the
formula only for it we do not hear the
sequence is 2 4 6 8 10 12 again let's
write 4 6 8 10 12 the difference is 2
here the difference is 2 2 8 10 - 10 12
do you see the difference is constant
that is true in all the cases so it is e
V now we can use the formula s n is
equal to N by 2 into U of A plus n minus
1 into D to use this formula we should
know n we should know a we should be
give 1 2 3 4 1 2 3 4 5 6 there are six
elements so n is going to sex the first
payment is true so a is equal to the
difference of element is 2 could D is
equal to 2 so we define the comma B just
replace this values n 0 to 6 here's you
can write s 6 is equal to 6 by 2 into 4
is 2 plus n minus 1 that is 6 minus 1
into D is 2 so this becomes 3 into 4
plus 5 into 2 is 10
so this becomes 14 EU 3 that is 4 into 3
is 4 d2 d2 and that is a pencil here the
question says the sum of n terms of 2 AP
they are to agree actually AP 1 and it
will be there to a be sum of n terms of
this array ratio 3 n plus 8 by 7 and
plus 15 we have to find the ratio of the
f12 number that means the question say
is s1 and because there is the first AP
by s 2 n second AP is 3 n plus 8 by 7 n
plus 50 this is the question says and
what you have to find we have to find t
1 to L by K to 12 correct this we have
to find because they are two different
if this is equal to what we have to 5 so
if you write this equation here s 1 n we
can also say this is nothing but n by 2
into 2 even plus n minus 1 D 1 this is s
1 s 2 we can say s 2 ends again n by 2
into 2 into plus n minus 1 D 2 this
ratio is they are saying is 3 n plus 8
by 7 n plus 25 this is what pushes is it
is cancel and making in below
so what we get here is right here in a 1
plus n minus 1 D 1 by 2 a 2 plus n minus
1 D 2 is equal to 3 n plus 8 by 7 and
five this is our equation 1 now what we
have to find is T 1 12 by T 2 12 alright
so this becomes even plus 12 minus 1 D
by D 1 by a 2 plus 12 minus 1 because P
n is equal to 8 plus n minus 1 D you
know the smaller now this becomes a 1
plus xi d 1 by 8 plus 11 D 2 is our
second equation so if we observe these
two equation properly a1 and d1 here
into D 2 so if we put the value of n is
equal to 23 and this becomes 23 minus 1
22 and this is 11 so first let's convert
this into to a 1/4 so also it will will
multiply to both new in time derivative
so what we get in right here actually to
a 1 plus 22 B 1 by 2 e 2 plus 22 D 2 so
this is what we have got now we see we
compare these two equations if you can
see you can say n minus 1 is equal to 22
if you can say n minus 1 if you can say
M minus 1 0 22 because this is n minus 1
this is what you do this is n minus plus
ready we can get the answer or we can
say n is equal to 23 put this sign this
function if you put n will go 23 to get
the answer so in this equation if you
put n 0 23 what we get is I am taking
this equation now so I am taking this
equation here so what I get to a 1 plus
23 minus 1 22 de 1 by a 2 plus 23 minus
1 22
Deepu this becomes three into 23 it is n
is 23 plus a by 7 into 23 2005 as well
what we get and if you solve this this
becomes change when is a 69 plus a 7
into 23 is so in 21 141 61 plus 25 you
solve this this becomes 77 and this
becomes 6 this becomes 6 plus 2 this is
this is 15 sorry this is 15 here this is
15 so 161 plus 15 you get 176 and now
you divide by 11 so them sevens this
become 1 & 6
so what you get is 7 by 16 that is the
answer what we have done we have just
used the formula of SN and we got this
ratio and then me a foot use the formula
of TN in Cantus ratio and then we
observe that if you put n minus 1 is
going to do 22 this animal 24 you will
get the answer so we have put L is equal
to 23 you wind up Dasia
let's say for example Navy say is income
per person is 2 lakh the first year that
he sees an increase of 10 key courier
the next 9 years and we want to find the
total income it is total amount he
receive in 20 years and also he's savvy
up an earlier so let's assume this to
Mack is well 200k just to make my life
simple and 10,000 is 10 K so we see the
income or will see the e/m here
here 1 2 3 4 5 6 . she's 19 years old
this is a year and now let me see income
the income in first year is 200 second
year is 200 key plus 10t this year is
200 she plus 20 this here is 200 k plus
30k in fifth year he hits 200 k plus 40
game simply keeping using 19 here he get
200 k plus a TD and he in 20th year he
get 200 k plus 19 year that is a pattern
because it see that every year is in
given in doing so we'll get this fun so
we can see that any year TN is nothing
but you hundred K plus n minus 1 into 10
K so that is his salary given here now
final salary up in 20 years very simple
we just put n is very ready
so T 20 is nothing but 200 K plus 20
minus 1 is 19 into 10 K that is 200 K
plus my in 190 K that is 390 he that is
nothing but 3 9 0 0 0 0 and this 3 lakh
mainly thousand that is a salary after
20 years now similarly if you have to
find the total amount which he has
earned in the past 20 years we have to
find s 20 correct s of n we know is n by
2 to a plus n minus 1
d so as of 20 will become 20 by 2 into 2
is the initial salary there is 200 K
plus n minus 1 and is 20 this is 1920 -
490 into D these increment every year
that is 10 give so this right here or s
of 20 is equal to 10 into 400 K plus 180
K that is or equal to 10 into 590 K this
becomes 5 9 0 0 ki and ki L right
right it was by 3 thousands three zeros
so that is 59 lag is the total salary
which he has on in the past 20 years
correct what we have done we know the
value of K that is 200 K you know the
value of D that is 10 K so we found T 20
that is 3 point 9 lakhs and s Wendy the
recipe relax thank you visit exam viacom
to watch free educational videos try
free online tests in the best quality
study materials study from the best
tutors and mentors
series part 6 is brought to you by exam
fear calm no more fear from exam before
watching this video please make sure
that you have washed video part 1 - Part
5 examples of soft thumbs so we had to
want to find the terms of EB we are told
to find the term some of the terms of
this sequence but we are not told where
there is an EP or chip first we need to
find whether VP or not so the sequence
is 2 4 6 7 e 10 the difference between
24 X - 4 into 6 is 2 6 7 is 1 7 8 is 1 8
in the list you see the difference is
not constant here it is 1 here it is 2
that means it is not an sin it is not an
AP and we have not learned anything else
till not now as of now we cannot solve
this question whether it is not an AP so
we can't serve because we know the
formula only for it we do not hear the
sequence is 2 4 6 8 10 12 again let's
write 4 6 8 10 12 the difference is 2
here the difference is 2 2 8 10 - 10 12
do you see the difference is constant
that is true in all the cases so it is e
V now we can use the formula s n is
equal to N by 2 into U of A plus n minus
1 into D to use this formula we should
know n we should know a we should be
give 1 2 3 4 1 2 3 4 5 6 there are six
elements so n is going to sex the first
payment is true so a is equal to the
difference of element is 2 could D is
equal to 2 so we define the comma B just
replace this values n 0 to 6 here's you
can write s 6 is equal to 6 by 2 into 4
is 2 plus n minus 1 that is 6 minus 1
into D is 2 so this becomes 3 into 4
plus 5 into 2 is 10
so this becomes 14 EU 3 that is 4 into 3
is 4 d2 d2 and that is a pencil here the
question says the sum of n terms of 2 AP
they are to agree actually AP 1 and it
will be there to a be sum of n terms of
this array ratio 3 n plus 8 by 7 and
plus 15 we have to find the ratio of the
f12 number that means the question say
is s1 and because there is the first AP
by s 2 n second AP is 3 n plus 8 by 7 n
plus 50 this is the question says and
what you have to find we have to find t
1 to L by K to 12 correct this we have
to find because they are two different
if this is equal to what we have to 5 so
if you write this equation here s 1 n we
can also say this is nothing but n by 2
into 2 even plus n minus 1 D 1 this is s
1 s 2 we can say s 2 ends again n by 2
into 2 into plus n minus 1 D 2 this
ratio is they are saying is 3 n plus 8
by 7 n plus 25 this is what pushes is it
is cancel and making in below
so what we get here is right here in a 1
plus n minus 1 D 1 by 2 a 2 plus n minus
1 D 2 is equal to 3 n plus 8 by 7 and
five this is our equation 1 now what we
have to find is T 1 12 by T 2 12 alright
so this becomes even plus 12 minus 1 D
by D 1 by a 2 plus 12 minus 1 because P
n is equal to 8 plus n minus 1 D you
know the smaller now this becomes a 1
plus xi d 1 by 8 plus 11 D 2 is our
second equation so if we observe these
two equation properly a1 and d1 here
into D 2 so if we put the value of n is
equal to 23 and this becomes 23 minus 1
22 and this is 11 so first let's convert
this into to a 1/4 so also it will will
multiply to both new in time derivative
so what we get in right here actually to
a 1 plus 22 B 1 by 2 e 2 plus 22 D 2 so
this is what we have got now we see we
compare these two equations if you can
see you can say n minus 1 is equal to 22
if you can say n minus 1 if you can say
M minus 1 0 22 because this is n minus 1
this is what you do this is n minus plus
ready we can get the answer or we can
say n is equal to 23 put this sign this
function if you put n will go 23 to get
the answer so in this equation if you
put n 0 23 what we get is I am taking
this equation now so I am taking this
equation here so what I get to a 1 plus
23 minus 1 22 de 1 by a 2 plus 23 minus
1 22
Deepu this becomes three into 23 it is n
is 23 plus a by 7 into 23 2005 as well
what we get and if you solve this this
becomes change when is a 69 plus a 7
into 23 is so in 21 141 61 plus 25 you
solve this this becomes 77 and this
becomes 6 this becomes 6 plus 2 this is
this is 15 sorry this is 15 here this is
15 so 161 plus 15 you get 176 and now
you divide by 11 so them sevens this
become 1 & 6
so what you get is 7 by 16 that is the
answer what we have done we have just
used the formula of SN and we got this
ratio and then me a foot use the formula
of TN in Cantus ratio and then we
observe that if you put n minus 1 is
going to do 22 this animal 24 you will
get the answer so we have put L is equal
to 23 you wind up Dasia
let's say for example Navy say is income
per person is 2 lakh the first year that
he sees an increase of 10 key courier
the next 9 years and we want to find the
total income it is total amount he
receive in 20 years and also he's savvy
up an earlier so let's assume this to
Mack is well 200k just to make my life
simple and 10,000 is 10 K so we see the
income or will see the e/m here
here 1 2 3 4 5 6 . she's 19 years old
this is a year and now let me see income
the income in first year is 200 second
year is 200 key plus 10t this year is
200 she plus 20 this here is 200 k plus
30k in fifth year he hits 200 k plus 40
game simply keeping using 19 here he get
200 k plus a TD and he in 20th year he
get 200 k plus 19 year that is a pattern
because it see that every year is in
given in doing so we'll get this fun so
we can see that any year TN is nothing
but you hundred K plus n minus 1 into 10
K so that is his salary given here now
final salary up in 20 years very simple
we just put n is very ready
so T 20 is nothing but 200 K plus 20
minus 1 is 19 into 10 K that is 200 K
plus my in 190 K that is 390 he that is
nothing but 3 9 0 0 0 0 and this 3 lakh
mainly thousand that is a salary after
20 years now similarly if you have to
find the total amount which he has
earned in the past 20 years we have to
find s 20 correct s of n we know is n by
2 to a plus n minus 1
d so as of 20 will become 20 by 2 into 2
is the initial salary there is 200 K
plus n minus 1 and is 20 this is 1920 -
490 into D these increment every year
that is 10 give so this right here or s
of 20 is equal to 10 into 400 K plus 180
K that is or equal to 10 into 590 K this
becomes 5 9 0 0 ki and ki L right
right it was by 3 thousands three zeros
so that is 59 lag is the total salary
which he has on in the past 20 years
correct what we have done we know the
value of K that is 200 K you know the
value of D that is 10 K so we found T 20
that is 3 point 9 lakhs and s Wendy the
recipe relax thank you visit exam viacom
to watch free educational videos try
free online tests in the best quality
study materials study from the best
tutors and mentors
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Nov 28, 2024 Last updated |
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