`a_1 = 0.375, a_(n + 1) = a_n + 0.27` Find the sum of the integers from -100 to 30.

Given: `a_1=0.375, a_(n+1)=a_n+0.27`

The equation for an arithmetic sequence is

`a_n=a_1+(n-1)d`

`a_n=0.375+(n-1)(0.27)`

`a_n=0.375+0.27n-.27`

`a_n=0.27n-.105`

`sum_(n=-100)^30 .27n+.105` 

The sum formula for an arithmetic sequence is

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

`n=131`

`a_1=.27(-100)+.105=-26.895`

`a_n=-.27(30)+.105=8.205`

`S_131=131/2(-26.895+8.205)`

`S_131=65.6(-18.69)`

`S_131=-1224.195`