Find the sum: −8 + −4 + 0 + ... + (−12+4n)

Answer 1

This is an arithmetic sequence.

This means that each term is obtained from the previous by adding a constant;

in your example the constant is 4.

In general, to sum an arithmetic sequence you multiply the number of terms

by the average between the first and last.

In your case you have n terms,

the first term is -8,

the last term is -12 + 4n.

So the sum is

n(-8 + (-12+4n))/2 = n(2n - 10)