Question

What is the sum of a 22-term arithmetic sequence where the first term is 56 and the last term is -28?

Answer 1

308

Explanation:

The sequence is {56+(n-1)d}, 2 = 1, 2, 3, ...,22, wher d is the common difference.

The last term (n=22) is `-28=56+21d`,
So, `d=-82/21=-4`.

The sum = `(22)(56)+(d+2d+3d,...+21d)=1232-(21)(22/2)(-4)`. using `1+2+3...+n=(n(n+1))/2`
The sum simplifies to 308.