Question

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

Answer 1

The value of the `30^(th)` 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^(th)` 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