Question

In an arithmetic progression, the fourth term is $8$ and the sum of $12$ terms is $156$. Find the value of '$p$' if the $p$ ${}^{th}$ term is $1000$.

• A. $200$
• B. $500$
• C. $300$
• D. $100$

Answer 1

The correct option is B $500$

Let first term be $a$ and common difference be $d$

$\therefore a+3d=8$ .....(1)

$\therefore \frac{12}{2}[2a+(12-1\left)d\right]=156$

$\Rightarrow 2a+11d=26$ .....(2)

From eq(1) and eq(2):

$a=2$ and $d=2$

Now,

$p^{th}$ term $=2+(p-1)2=1000$

$\Rightarrow (p-1)2=998$

$\Rightarrow (p-1)=499$

$\therefore p=500$

(Ans = B)