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

Mar 17, 2018

Hence color(green)(a_n = a_1 + (n-1) * d is the general form for the ${n}^{t h}$ term.

Explanation:

Given : ${a}_{1} = 0 , d = - \left(\frac{2}{3}\right)$

${a}_{2} = {a}_{1} + d = 0 - \frac{2}{3} = - \frac{2}{3}$

${a}_{3} = {a}_{2} + d = {a}_{1} + 2 d = {a}_{1} + \left(3 - 1\right) d = 0 - \frac{4}{3} = - \frac{4}{3}$

${a}_{4} = {a}_{3} + d = {a}_{1} + 3 d = {a}_{1} + \left(4 - 1\right) d = 0 - \frac{6}{3} = - 2$

Hence ${a}_{n} = {a}_{1} + \left(n - 1\right) \cdot d$ is the general form for the ${n}^{t h}$ term.