Question

How do you find the sum of each arithmetic series `Sigma (2n+3)` from n=1 to 12?

Answer 1

`sum_(n=1)^12 (2n+3)= 180`

Explanation:

The sum of a series is the average term multiplied by the number of terms. When the series is arithmetic, the average term is the same as the average of the first and last term.

So:

`sum_(n=color(blue)(1))^color(blue)(12) (2n+3) = 1/2((2(color(blue)(1))+3)+(2(color(blue)(12))+3))*12`

`color(white)(sum_(n=1)^12 (2n+3)) = 6(5+25) = 6*30 = 180`