# What is the 30th term of the arithmetic series 2, 5, 8, … ?

May 6, 2018

${a}_{30} = 89$

#### Explanation:

Given: arithmetic series $2 , 5 , 8$

arithmetic series have the form: ${a}^{n} = {a}_{1} + \left(n - 1\right) d$

$d =$ the common difference

$d = {a}_{2} - {a}_{1} = {a}_{3} - {a}_{2} = 8 - 5 = 3$

${a}^{n} = 2 + 3 \left(n - 1\right)$

To find the 30th term, let $n = 30$:

${a}_{30} = 2 + 3 \left(30 - 1\right) = 2 + 3 \left(29\right) = 2 + 87 = 89$