Question

Given the Arithmetic series A1+A2+A3+A4

13 + 16 + 19 + 22 + . . . + 67
What is the value of sum?

Answer 1

`S _(19) = 760`

Explanation:

`a1 = 13 \\ a2 = 16 \\ d = a2 - a1 = 16 - 13 = 3 \\ d = 3 \\ a _(n) = l = 67 \\`

now,

`a _(n) = a + (n - 1) * d \\ 67 = 13 + (n - 1) * 3 \\ 67 = 13 + 3n - 3 \\ 67 - 13 + 3 = 3n \\ 57 = 3n \\ 3n = 57 \\ \\ n = (57)/(3) \\ \\ n = 19`

now the sum of the numbers

`S _(n) = (n)/(2) (a + l) \\ \\ S _(19) = (19)/(2) (13 + 67) \\ \\ S _(19) = (19)/(2) (80) \\ \\ S _(19) = (19)/(2) * 80 \\ \\ S _(19) = 19 * 40 \\ S _(19) = 760`