Question

What is the sum of the arithmetic sequence 22, 13, 4?

Answer 1

`22 + 13 + 4 = 39`. A very straightforward answer.

However, if one wishes to find it that way (the stupid way), then first notice that this is a simple arithmetic series. Use the formula `S = n/2 (a_1 + a_{\text{n}))` or the formula `S = n/2 (2a_1 + (n-1)d)` where `a_1` is the first term, `a_n` is the last term, `d` is the common difference, `n` is the number of terms in your series.

Note that both of these are equivalent since `a_n = a_1 + (n- 1)d`.

`S = 3/2 (22 + 4) = 39` or `S = 3/2 ( 2\cdot 22 - 9\cdot 2) = 39.`