Question

what is the sum of the first twelve terms of an A.P, whose first term is 15 and the common different is 13.​

Answer 1

Given:

• First term of AP is 15
• Common difference is 13
• Term is 12

To find:

• Sum of first twelve term of AP

Solution:

We are given that First term is 15 and common difference between them is 13.

To find Sum of n term of AP, we know that :

$\huge{\boxed{\large{\sf{S_n = \frac{n}{2}\bigg[2a +(n - 1)×d\bigg] }}}}$

Where,

• ${\sf{S_n}}$ = sum of n term of AP
• n = Number of terms
• a = First term
• d = common difference

Putting values:-

$\large{\sf{s_n = \frac{n}{2}\bigg[2a +(n - 1)×d\bigg] }}$

$\large{\implies{\sf{S_{12} = \frac{12}{2}\bigg[2×15 +(12- 1)×13\bigg]}}}$

$\large{\implies{\sf{S_{12}= 6 \bigg[30+(11×13)\bigg]}}}$

$\large{\implies{\sf{S_{12}= 6\bigg[30+143\bigg]}}}$

$\large{\implies{\sf{S_{12}=6× 173}}}$

$\large{\implies{\sf{S_{12}= 1038}}}$

Therefore,

• Sum of first 12 term of AP is 1038