Question

What is the sum of the first $12$ terms of an arithmetic progression if the $3^{rd}$ term is $-13$ and the $6^{th}$ term is $-4$?

• A. $67$
• B. $45$
• C. $-30$
• D. $-48$

Answer 1

The correct option is C $-30$

Let the first term be $a$ and $d$ be the common difference
$3^{rd}term=a+2d$ and $6^{th}term=a+5d$
$(a+5d)=-4$ ......(1)

$(a+2d)=-13)$ ......(2)

Solving (1) &(2), we get
$d=3,a=-19$
Sum of first $12terms=\frac{n}{2}[2a+(n-1)\times d]=\frac{12}{2}[2\times (-19)+(12-1\left)3\right]=-30$.