Question

Find the sum of the first 12 terms of the sequence. Show all work for full credit. 1, -4, -9, -14, . . . (2 points)

Answer 1

The sum is = -318

Explanation:

See the attached image

Answer 2

`S_n=` -348

Explanation:

We are given the following arithmetic sequence and we are to find the sum of its first 12 terms:

1, -4, -9, -14, . . .

For that, we will use the formula for the sum of the arithmetic mean:

`S_n=(n)/(2) (a_1+a_n)`

We know the value of the first term (
`a_n`) but we need to find the value of
`a_(12)`. So we will use the following formula:

`a_(12)=a_1+(n-1)d`

`a_(12)=(-4)+(12-1)(5)`

`a_(12)=-59`

Substituting these values in the sum formula to get:

`S_n=(12)/(2) (1+(-59))`

`S_n=` -348