Question

if the sum of first n terms of an a.p n2 then find its 10th term​

Answer 1

$\underline{\textbf{Given:}}$

$\textsf{Sum of first 'n' terms of an A.P is}\;\mathsf{n^2}$

$\underline{\textbf{To find:}}$

$\textsf{10 th term of the A.P}$

$\underline{\textbf{Solution:}}$

$\textsf{Sum of first n terms}\mathsf{=n^2}$

$\implies\mathsf{S_n=n^2}$

$\textsf{clearly}$

$\implies\mathsf{t_n=S_n-S_{n-1}}$

$\implies\mathsf{t_{10}=S_{10}-S_9}$

$\implies\mathsf{t_{10}=10^2-9^2}$

$\implies\mathsf{t_{10}=100-81}$

$\implies\boxed{\mathsf{t_{10}=19}}$