Question

How do you find the sum of the series `12i` from i=0 to i=5?

Answer 1

You can add `12(0) + 12(1) + 12(2) + 12(3) + 12(4) + 12(5)`, or recognize a pattern and apply a formula.

Explanation:

What type of sequence is `0, 12, 24,36, 48, 60`?
If it is arithmetic, then we have a nice formula to apply!
Turns out that it is arithmetic, with a first term `a_1` = 0, `a_6=60` and d = 12, with n = 6 terms.

`S_6=6/2(0+60)` = 3*60 = 180.