###
**What is the sum of the first 12 terms of an arithmetic progression if the 3rd term is -13 and the 6th term is -4?**

A. 67
B. 45
C. -30
D. -48
**Answer: Option C**

## Show Answer

Solution(By Apex Team)

$\begin{aligned}&T_3=a+2d=-13\ldots\ldots\text{ (1) }\\
&T_6=a+5d=-4\ldots\text{ (2) }\\
&\text{ on solving (1) and }\\
&d=3\&a=-19\\
&S_n=\frac{n}{2}[2a+(n-1)d]\\
&S_{12}=\frac{12}{2}[2(-19)+(12-1)(3)]\\
&S_{12}=(6)[-38+33]\\
&S_{12}=-30\end{aligned}$

## Related Questions On Progressions

### How many terms are there in 20, 25, 30 . . . . . . 140?

A. 22B. 25

C. 23

D. 24

### Find the first term of an AP whose 8th and 12th terms are respectively 39 and 59.

A. 5B. 6

C. 4

D. 3

### Find the 15th term of the sequence 20, 15, 10 . . .

A. -45B. -55

C. -50

D. 0

### The sum of the first 16 terms of an AP whose first term and third term are 5 and 15 respectively is

A. 600B. 765

C. 640

D. 680