Question

Find the sum of the arithmetic sequence.

-10, -7, -4, -1, 2, 5, 8

Answer 1

there is a formula for this; but also a very handy shortcut for shorter sequences.

write the sequence out, and the do the same in reverse order

-10 -7 -4 -1 2 5 8
8 5 2 -1 -4 -7 -10
add each of the columns up, and you get -2 in each one. there are 7 items in the series, so the total of TWO series is 7 x -2 = -14, the total for ONE series is - 7.

of course, once you know this, you don't have to write anything out. just do it.

if you remember this pattern, you will remember the basis of the derivation of the formula for summing series too.