# What is the 30th term of the arithmetic series 2+7+12+17+...?

Dec 18, 2016

The value of the ${30}^{t h}$ term in this arithmetic progression is 147

#### Explanation:

You are looking at what is called an arithmetic progression as the terms change by adding a common value (or common difference).

It is typical to write ${t}_{n}$ as the ${n}^{t h}$ term in the progression, and $d$ as the common difference. Then

${t}_{n}$ = ${t}_{1}$ + ($n$ - 1) $d$

Since, in this case, the common difference is $d$= 5 and $n$ = 30 is the term we are looking for

${t}_{n}$ = 2 + (30 - 1) 5 = 2 + 145 = 147