# 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

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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 $0$.

Updated on 10-Oct-2022 13:27:27