Question

Find the sum of the first 56 terms of the following sequence {-8, -1, 6, ...}

A. 10,332
B. 1,344
C. 10,584

Answer 1

A

Explanation:

Given sequence
`-8,\ -1,\ 6,\ ...`

In this sequence,

`a_1=-8\\ \\a_2=-1\\ \\a_3=6\\ \\...`

Hence,

`d=a_2-a_1=-1-(-8)=7\\ \\d=a_3-a_2=6-(-1)=7`

Find 56th term:

`a_(n)=a_1+(n-1)\cdot d\\ \\a_(56)=-8+(56-1)\cdot 7\\ \\a_(56)=-8+385\\ \\a_(56)=377`

The sum of 56 terms is

`S_n=(a_1+a_n)/(2)\cdot n\\ \\S_(56)=(-8+377)/(2)\cdot 56=(369)/(2)\cdot 56=369\cdot 28=10,332`