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Nth term of AP Video Lecture - Class 10
FAQs on Nth term of AP Video Lecture - Class 10
| 1. What is the formula to find the nth term of an arithmetic progression (AP)? |  |
Ans. The formula to find the nth term of an AP is given by:
an = a1 + (n - 1)d
where an is the nth term, a1 is the first term, n is the position of the term, and d is the common difference.
| 2. How do I find the common difference of an AP if only the first term and nth term are given? | |
Ans. To find the common difference of an AP when only the first term (a1) and nth term (an) are given, we can use the formula:
d = (an - a1) / (n - 1)
where d is the common difference.
| 3. Can the common difference of an AP be negative? | |
Ans. Yes, the common difference of an AP can be negative. The common difference represents the constant difference between consecutive terms, so it can be positive, negative, or zero.
| 4. What is the significance of the nth term in an AP? | |
Ans. The nth term in an AP represents the value of the term at position 'n'. It helps in determining the value of any term in the arithmetic sequence without having to compute all the preceding terms.
| 5. How can I identify if a given sequence is an arithmetic progression? | |
Ans. To identify if a given sequence is an arithmetic progression, you need to check if the difference between consecutive terms is constant. If the difference remains the same throughout the sequence, it is an arithmetic progression.
Text Transcript from Video
hello friends this video on arithmetic
progressions part 5 is brought to you by
exam fear calm no more fear from exam
before watching this video please make
sure that you have watched part 1 - part
4 for a given AP if you have to find the
NS term that is your advice n is nothing
but a plus n minus 1 see the AP I have
showed you is nothing but a a plus D a
plus 2b
a + 3 d a plus 4 D and so on correct
this term is called a 1 this is a 2 this
is a 3 that is third down this is fourth
term
this is fifth term and this is min so on
now if we have to find the general
formula what we do here you see
observation what if you see a 1 I can
write as nothing but even is 8 that is a
plus this is 1 1 minus 1 in D that is 0
into D a 2 if you see I can write as a
plus here - well put here 2 - 1 - D a 3
I can write as nothing but a plus 3
minus 1 into D Y because a 3 is a plus 2
D similarly a 4 I can write as ay plus 4
minus 1 D and AFI I can write it has
nothing but a plus 5 minus 1 D it's
correct so if you see that if I want to
write a common formula I can write ANS
nothing but a plus because in all the
form Y is common plus is common and here
you see one two three four five six one
two three four five this is nothing but
by the value of n n plus n1 is common in
n minus 1 into D see from this only
emailing a one is a plus one minus one
in versus a 2 is 8 plus 2 minus 1 d a 3
is a plus 3 minus 1 D so we have this
this we know this is the common notation
for a anything from this we observe that
for any term a n n is nothing but a plus
n minus 1 this is my general formula
practically we can implement also but
I'll give you an example so let's
suppose we have this lady her name is it
suppose Sita Sita gets a salary of let's
suppose 1,000 rupees per month and every
month she gets increment of 100 degrees
so we have seen that such scenario is an
AP so her salary will be after first
year will be 1,000 second will be 1100
and then it will be 1290 1300 and there
will be 1000 phone and while after every
year she's getting an agreement of
hundred rupees correct so the salaries
in this form now let's suppose I want to
find her salary in third year so I'll
say e3 is nothing but 8 plus n is going
to 3 minus 1 into T DS hundred that will
be 1,000 plus 2 into hundred and that
will be 12 in it and if you see this
value and this value which we got this
sink the series also if you find or
solving something like this 1,000 1,100
1,200 1,300 three years or surveys this
much and using my formula also we are
getting our salaries same that is 1200
so we can see that the formula is cut
please remember this formula is a very
crucial formula for any AP term a and is
a plus n minus 1 D where a is the first
term and as this n wishes a N and D is
the common difference but till now what
we have concluded the conclusion is for
any a be a NS a plus n minus 1 D where n
this n F term a is first term and is
and D is a common difference en is also
called the general term of AP and if
they are M comes in AP then am
represents the last obviously because
they are M term only let's go there five
terms only in the AP right it suppose
one two three four five this is also a P
actually with the common difference
month the only five term then this term
be the last term so am will represent
the last term and the last term is the
red wife let's take my example here we
have the fill in the blind we have been
given a D and en and some things are
missing actually so in the first part
this first the second is the curve this
is would be nice especially suppose en
is missing the formula we know that and
is a plus n minus 1 D this formula we
know correct so n is going to a plus n
minus 1 T so a is 7 here given here plus
n is 8 here 8 minus 1 and D is 3 all
right
this becomes 7 plus 7 into 3 that is 7
plus 21 there is no different when you
so ans 20 a la seconde also will use the
same formula ans 8 plus n minus 1 T and
is minus 18 minus VD is equal to a sorry
n is 0 n 0 0 is going to a is minus 18
plus n repeat this n is going to a plus
n minus 1 d n is nothing but 0 0 is
equal to a is nothing but minus 18 plus
n is nothing but 10
- Maru correct solid D is equal to PD in
my mind that is true so d is good route
to his money answer in part three you
see I like you here again a n is equal
to a plus n minus 1 D n is going 2-5
given here is equal to a is not given
plus and is 18 given here minus 1 into D
is minus 3 correct
so again a is nothing but 17 into 3 by 7
teen into 13 plus 4 this is minus 5 this
becomes 51 minus 5 that is 14 so the
cells or d C's let us take this for
example the N is going to 8 plus n minus
1 the same form I will use here n is
equal to 36 given 3.6 it's going to a is
minus 18 point length plus n minus K at
the point in 2d DS keep on right or we
get n minus 1 is nothing but 3 point 6
plus 18.9 by 0.5 this is nothing but
penny 2 point 5 by 2 point 5 we get this
is equal to 9 HP all we get n is good
too and so here we have an event let's
take the last native again with the same
formula n is equal to a plus n minus 1 D
here n is not given a is given 3 point 5
plus n is given one not 5 what 5 minus 1
into D 0 will come 0 so a n will come
out to be three point five itself
so this is three point one as we have
filled in all the blanks very simple
just use the formula a n is equal to a
plus n minus 1
please remember this formula very
crucial formula a n is equal to a plus n
minus 1 into D correct where n is the nm
term is the first term it is the let's
take some example we have to find the N
of jump of this AP now looking at the AP
we can say that a is equal to 10 and the
difference is 3 actually minus 3 so D is
equal to minus all right so we know that
a is equal to 10 and D is equal to minus
this thing we know now very simple a n
is going to a plus n minus 1 D correct a
is 10 plus n is nothing but 30 we are
trying for thirty eight thirty thirty
minus 1 into T is minus 3 that is 10
plus 29 into minus 3 that is nothing
worth 10 minus 87 and that's come out -
mmm say so we can say that thirtieth
term of this AP will be minus 7 itself
very simple we found the value of a we
found the value of T use the formula a n
is going to be 8 plus M s bundy to get
the answer
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 and screen
progressions part 5 is brought to you by
exam fear calm no more fear from exam
before watching this video please make
sure that you have watched part 1 - part
4 for a given AP if you have to find the
NS term that is your advice n is nothing
but a plus n minus 1 see the AP I have
showed you is nothing but a a plus D a
plus 2b
a + 3 d a plus 4 D and so on correct
this term is called a 1 this is a 2 this
is a 3 that is third down this is fourth
term
this is fifth term and this is min so on
now if we have to find the general
formula what we do here you see
observation what if you see a 1 I can
write as nothing but even is 8 that is a
plus this is 1 1 minus 1 in D that is 0
into D a 2 if you see I can write as a
plus here - well put here 2 - 1 - D a 3
I can write as nothing but a plus 3
minus 1 into D Y because a 3 is a plus 2
D similarly a 4 I can write as ay plus 4
minus 1 D and AFI I can write it has
nothing but a plus 5 minus 1 D it's
correct so if you see that if I want to
write a common formula I can write ANS
nothing but a plus because in all the
form Y is common plus is common and here
you see one two three four five six one
two three four five this is nothing but
by the value of n n plus n1 is common in
n minus 1 into D see from this only
emailing a one is a plus one minus one
in versus a 2 is 8 plus 2 minus 1 d a 3
is a plus 3 minus 1 D so we have this
this we know this is the common notation
for a anything from this we observe that
for any term a n n is nothing but a plus
n minus 1 this is my general formula
practically we can implement also but
I'll give you an example so let's
suppose we have this lady her name is it
suppose Sita Sita gets a salary of let's
suppose 1,000 rupees per month and every
month she gets increment of 100 degrees
so we have seen that such scenario is an
AP so her salary will be after first
year will be 1,000 second will be 1100
and then it will be 1290 1300 and there
will be 1000 phone and while after every
year she's getting an agreement of
hundred rupees correct so the salaries
in this form now let's suppose I want to
find her salary in third year so I'll
say e3 is nothing but 8 plus n is going
to 3 minus 1 into T DS hundred that will
be 1,000 plus 2 into hundred and that
will be 12 in it and if you see this
value and this value which we got this
sink the series also if you find or
solving something like this 1,000 1,100
1,200 1,300 three years or surveys this
much and using my formula also we are
getting our salaries same that is 1200
so we can see that the formula is cut
please remember this formula is a very
crucial formula for any AP term a and is
a plus n minus 1 D where a is the first
term and as this n wishes a N and D is
the common difference but till now what
we have concluded the conclusion is for
any a be a NS a plus n minus 1 D where n
this n F term a is first term and is
and D is a common difference en is also
called the general term of AP and if
they are M comes in AP then am
represents the last obviously because
they are M term only let's go there five
terms only in the AP right it suppose
one two three four five this is also a P
actually with the common difference
month the only five term then this term
be the last term so am will represent
the last term and the last term is the
red wife let's take my example here we
have the fill in the blind we have been
given a D and en and some things are
missing actually so in the first part
this first the second is the curve this
is would be nice especially suppose en
is missing the formula we know that and
is a plus n minus 1 D this formula we
know correct so n is going to a plus n
minus 1 T so a is 7 here given here plus
n is 8 here 8 minus 1 and D is 3 all
right
this becomes 7 plus 7 into 3 that is 7
plus 21 there is no different when you
so ans 20 a la seconde also will use the
same formula ans 8 plus n minus 1 T and
is minus 18 minus VD is equal to a sorry
n is 0 n 0 0 is going to a is minus 18
plus n repeat this n is going to a plus
n minus 1 d n is nothing but 0 0 is
equal to a is nothing but minus 18 plus
n is nothing but 10
- Maru correct solid D is equal to PD in
my mind that is true so d is good route
to his money answer in part three you
see I like you here again a n is equal
to a plus n minus 1 D n is going 2-5
given here is equal to a is not given
plus and is 18 given here minus 1 into D
is minus 3 correct
so again a is nothing but 17 into 3 by 7
teen into 13 plus 4 this is minus 5 this
becomes 51 minus 5 that is 14 so the
cells or d C's let us take this for
example the N is going to 8 plus n minus
1 the same form I will use here n is
equal to 36 given 3.6 it's going to a is
minus 18 point length plus n minus K at
the point in 2d DS keep on right or we
get n minus 1 is nothing but 3 point 6
plus 18.9 by 0.5 this is nothing but
penny 2 point 5 by 2 point 5 we get this
is equal to 9 HP all we get n is good
too and so here we have an event let's
take the last native again with the same
formula n is equal to a plus n minus 1 D
here n is not given a is given 3 point 5
plus n is given one not 5 what 5 minus 1
into D 0 will come 0 so a n will come
out to be three point five itself
so this is three point one as we have
filled in all the blanks very simple
just use the formula a n is equal to a
plus n minus 1
please remember this formula very
crucial formula a n is equal to a plus n
minus 1 into D correct where n is the nm
term is the first term it is the let's
take some example we have to find the N
of jump of this AP now looking at the AP
we can say that a is equal to 10 and the
difference is 3 actually minus 3 so D is
equal to minus all right so we know that
a is equal to 10 and D is equal to minus
this thing we know now very simple a n
is going to a plus n minus 1 D correct a
is 10 plus n is nothing but 30 we are
trying for thirty eight thirty thirty
minus 1 into T is minus 3 that is 10
plus 29 into minus 3 that is nothing
worth 10 minus 87 and that's come out -
mmm say so we can say that thirtieth
term of this AP will be minus 7 itself
very simple we found the value of a we
found the value of T use the formula a n
is going to be 8 plus M s bundy to get
the answer
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 and screen
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Nov 16, 2024 Last updated |
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