Question

What is the sum of the arithmetic sequence 140, 134, 128…, if there are 33 terms?

Answer 1

We first work out the 33th term, the general formula for a sequence like this being `a_n=a_0+nxxd`, `d` being the difference.

Explanation:

Every term is the previous plus or minus the differnce `d=-6`. So to get to the 33th term we take 32 of these steps (remember we call the first term `a_0` and the 33th is thus `a_32` -- remember this!!):

`a_32=140+32xx(-6)=-52`

The sum is `33xx` the average, or

`sum=33xx(140+(-52))/2=33xx88/2=1452`