Question

What is the sum of the arithmetic sequence 153, 139, 125, …, if there are 22 terms?

Answer 1

$a_1=153\\a_2=139\\a_3=125\\\vdots\\\\d=a_2-a_1\to d=139-153=-14$

The formula of the sum of the arithmetic sequence:

$S_n=\dfrac{2a_1+(n-1)d}{2}\cdot n$

We have:

$a_1=153\\d=-14\\n=22$

substitute

$S_{22}=\dfrac{2\cdot153+(22-1)\cdot(-14)}{2}\cdot22=(306+21\cdot(-14))\cdot11=132$