# The sum of the first n terms of an A.P. is $4n^2 + 2n$. Find the nth term of this A.P.

Given:

The sum of first $n$ terms of an A.P. is $4n^{2} +2n$.

To do:

We have to find the $n^{th}$ term of the given A.P.

Solution:

$S_{n} =4n^{2} +2n$

For $n=1,\ S_{1} =4\times 1^{2} +2\times 1=4+2=6$

Therefore, first term $a=6$

For $n=2,\ S_{2} =4\times 2^{2} \ +2\times 2=16+4=20$

$\therefore$ Second term of the A.P.$=S_{2} -S_{1}$

$=20-6$

$=14$

Common difference of the A.P., $d=$second term $-$ first term

$=14-6=8$

We know that,

$a_{n}=a+(n-1)d$

$\therefore a_n=6+( n-1) \times 8$

$=6+8n-8$

$=8n-2$

Therefore, the $n^{th}$ term of the given A.P. is $8n-2$.

- Related Articles
- The sum of first n terms of an A.P. is $3n^2 + 4n$. Find the 25th term of this A.P.
- The sum of first n terms of an A.P. is $5n – n^2$. Find the nth term of this A.P.
- The sum of first n terms of an A.P. is $3n^{2} +4n$. Find the $25^{th}$ term of this A.P.
- The nth term of an A.P. is given by $(-4n + 15)$. Find the sum of first 20 terms of this A.P.
- The sum of the first n terms of an A.P. is $3n^2 + 6n$. Find the nth term of this A.P.
- Find the $5^{th}$ term of an A.P. of $n$ terms whose sum is $n^2−2n$.
- If the sum of the first $2n$ terms of the A.P. $2,\ 5,\ 8\ ..$ is equal to the sum of the first $n$ terms of the A.P. $57,\ 59,\ 61,\ ...$, then find $n$
- The sum of first $m$ terms of an A.P. is $4m^2 – m$. If its $n$th term is 107, find the value of $n$. Also, find the 21st term of this A.P.
- If the sum of first $n$ terms of an A.P. is $n^2$, then find its 10th term.
- Find the sum of the first 25 terms of an A.P. whose nth term is given by $a_n = 2 – 3n$.
- If the sum of the first $n$ terms of an A.P. is $4n – n^2$, what is the first term? What is the sum of first two terms? What is the second term? Similarly, find the third, the tenth and the $n$th terms.
- The sum of first $n$ terms of an A.P. whose first term is 8 and the common difference is 20 is equal to the sum of first $2n$ terms of another A.P. whose first term is $-30$ and common difference is 8. Find $n$.
- In an A.P. the sum of $n$ terms is $5n^2−5n$. Find the $10^{th}$ term of the A.P.
- The sum of first $n$ terms of an A.P. is $5n^2 + 3n$. If its $m$th term is 168, find the value of $m$. Also, find the 20th term of this A.P.
- The sum of the first 7 terms of an A.P. is 63 and the sum of its next 7 terms is 161. Find the 28th term of this A.P.

##### Kickstart Your Career

Get certified by completing the course

Get Started