Question

How do you find the formula for `a_n` for the arithmetic sequence `a_1=0, d=-2/3`?

Answer 1

Hence `color(green)(a_n = a_1 + (n-1) * d` is the general form for the `n^(th)` term.

Explanation:

Given : `a_1 = 0, d = -(2/3)`

`a_2 = a_1 + d = 0 - 2/3 = -2/3`

`a_3 = a_2 + d = a_1 + 2d = a_1 + (3-1) d= 0 - 4/3 = -4/3`

`a_4 = a_3 + d = a_1 + 3d = a_1 + (4-1) d= 0 - 6/3 = -2`

Hence `a_n = a_1 + (n-1) * d` is the general form for the `n^(th)` term.