Question

What is the sum of the first five terms of the series 7 12 17 ...

Answer 1

It's an arithmetic series.
The sum of the first n terms of an arithmetic series:

`S_n=(n(a_1+a_n))/(2)`


`7, 12, 17,... \\ \\ a_1=7 \\ d=a_2-a_1=12-7=5 \\ a_5=a_3+2d=17+2 * 5=17+10=27 \\ \\ S_5=(5(7+27))/(2)=(5 * 34)/(2)=5 * 17=85`

The sum of the first five terms is 85.