Question

Given the Arithmetic series A1+A2+A3+A4

12 + 17 + 22 + 27 + . . . + 107
What is the value of sum?

Answer 1

`1190`

Explanation:

`a1 = 12 \\ a2 = 17 \\ d = a2 - a1 = 17 - 12 = 5 \\ d = 5 \\ l = 107 \\`

`a _(n) = l = 107`

`a _(n) = a + (n - 1) * d \\ 107 = 12 + (n - 1) * 5 \\ 107 = 12 + 5n - 5 \\ 107 + 5 - 12 = 5n \\ 100 = 5n \\ 5n = 100 \\ \\ n = (100)/(5) = 20 \\ \\ n = 20`

now, sum of total numbers

`S _(n) = (n)/(2) (a + l) \\ \\ S _(20) = (20)/(2) (12 + 107) \\ \\ S _(20) = 10(119) \\ S _(20) = 10 * 119 \\ S _(20) = 1190`