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=(2a_1+(n-1)d)/(2)\cdot n`

We have:

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

substitute

`S_(22)=(2\cdot153+(22-1)\cdot(-14))/(2)\cdot22=(306+21\cdot(-14))\cdot11=132`