Question

If the sum of n terms of an A.P. is 2n^2 + 5n, then find the 4th term

Answer 1

Answer:

Step-by-step explanation:

1st term=2×1^2+5×1=7

2nd term=2×2^2+5×2=18

18-7=11

Then 3rd term=11+4=15

4th term= 15+4=19

Answer 2

Given:-

Sn = 2n² + 5n

To find :-

4 th term .

Solution:-

Replacing n by (n - 1) ,we get

S(n -1) = $2 {(n - 1)}^{2} + 5(n - 1)$

$\implies$ $2( {n}^{2} + 1 - 2n) + 5(n - 1)$

$\implies$ $s (n - 1) = 2 {n}^{2} + 2 - 4n + 5n - 5$

$\implies$ $s(n - 1) = 2 {n}^{2} + n - 3$

Now,

$\boxed{\sf</strong><strong>\</strong><strong>r</strong><strong>e</strong><strong>d</strong><strong>{ </strong><strong>an</strong><strong> </strong><strong>=</strong><strong> </strong><strong>Sn</strong><strong> </strong><strong>-</strong><strong> </strong><strong>S(</strong><strong>n-1</strong><strong>)</strong><strong> </strong><strong>}}$

$\implies$ $an = 2 {n}^{2} + 5n - (2 {n}^{2} + n - 3)$

$\implies$ $an = 2 {n}^{2} + 5n - 2{n}^{2} - n + 3$

$\implies$ $an = 4n + 3$

put n = 4 we get,

$\implies$ $a4 = 4 \times 4 + 3$

$\implies$ $a4 = 19$

hence, the 4 th term of A. P is 19.