Question

Sn is 5n^2+3n find the n term and also find the 10 term

Answer 1

Hope this help you.

Answer 2

Answer:-

nth term is 10n-2

10th term = 98

Given that :-

Sum of n terms of Ap is 5n²+3n

To find :-

n and 10th term of AP

EXPLANATION :-

$s_n =5 {n}^{2} + 3n \\ \\ \\s_{n - 1} = 5 {(n - 1)}^{2} + 3(n - 1) \\ \\ \\ = 5( {n}^{2} + 1 - 2n) + 3n - 3 \\ \\ = 5 {n}^{2} - 10n + 5 + 3n - 3 \\ \\ = 5 {n}^{2} - 7n + 2$

Now,

$t_n = s_n - s_{n - 1}$

Putting down the values in the above formula :-

$t_n = 5 {n}^{2} + 3n - 5 {n}^{2} + 7n - 2 \\ \\ \\ = 10n - 2$

So,

The nth term of AP is 10n - 2

Now ,

10th term will be 10(10)-2 = 100-2 = 98