###
**What is the sum of the following series? -64, -66, -68, ……, -100**

A. -1458
B. -1558
C. -1568
D. -1664
**Answer: Option B**

## Show Answer

Solution(By Apex Team)

First term is -64. The common difference is -2. The last term is -100.
Sum of the first n terms of an AP =
$\begin{aligned}\frac{n}{2}\left[2a_1+(n-1)d\right]\\
\end{aligned}$
To compute the sum, we know the first term a1 = -64 and the common difference d = -2.
We do not know the number of terms n. Let us first compute the number of terms and then find the sum of the terms.
$\begin{array}{l}a_n=a_1+(n-1)d\\
-100=-64+(n-1)(-2)\end{array}$
Therefore, n = 19
Sum =
$\begin{aligned}S_n&=\frac{19}{2}[2(-64)+(19-1)(-2)]\\
S_n&=\frac{19}{2}[-128-36]\\
S_n&=19\times(-82)\\
S_n&=-1558\end{aligned}$

## 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