Choose the correct answer from the given four options:
If the first term of an $ \mathrm{AP} $ is $ -5 $ and the common difference is 2 , then the sum of the first 6 terms is
(A) 0
(B) 5
(C) 6
(D) 15

Given:

The first term of an \( \mathrm{AP} \) is \( -5 \) and the common difference is 2.

To do:

We have to find the sum of the first 6 terms. 

Solution:

First term $a_1 = a= -5$

Common difference $d =2$

We know that,

Sum of the $n$ terms of an AP is $S_n=\frac{n}{2}[2a+(n-1)d]$

Therefore,

$S_6= \frac{6}{2}[2(-5)+(6-1)2]$

$= 3(-10+10)$

$= 0$

The sum of the first 6 terms of the AP is $0$. 

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Updated on: 10-Oct-2022

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