Question

The sum of 'n' terms of an arithmetic sequence is given by $S_n=n(5n-3)$. What is its $p^{th}$ term?

• A. $p(5p-3)$
• B. $5p-3$
• C. $2(5p-4)$
• D. $5p-7$

Answer 1

The correct option is C $2(5p-4)$

Given:

$S_n=n(5n-3)$

$\therefore S_p=p(5p-3)$

$\therefore S_{p-1}=(p-1)\left[5\right(p-1)-3]=(p-1)(5p-8)$

$t_p=p^{th}$ term

$\therefore t_p=S_p-S_{p-1}$

$=p(5p-3)-(p-1)(5p-8)$

$=5p^2-3p-5p^2+8p+5p-8$

$=10p-8$

$=2(5p-4)$ (Ans $\to$ C)