# Thread: What's the formula for finding the terms in an arithmetic series?

1. ## What's the formula for finding the terms in an arithmetic series?

Here's the math problem....

In an arithmetic series, the terms of the series are equally spread out. For example, in 1+5+9+13+17, consecutive terms are 4 apart. If the first term in an arithmetic series is 3, the last term is 136, and the sum is 1,390, what are the first 3 terms?

2. ## Re: What's the formula for finding the terms in an arithmetic series?

Originally Posted by krstybrght
Here's the math problem....

In an arithmetic series, the terms of the series are equally spread out. For example, in 1+5+9+13+17, consecutive terms are 4 apart. If the first term in an arithmetic series is 3, the last term is 136, and the sum is 1,390, what are the first 3 terms?
$t_n = 136 = 3 + (n-1)d$ .... (1)

$S_n = 1390 =$ substitute formula for sum of n terms of an arithmetic series (look it up in your textbook or class notes) .... (2)

Solve equations (1) and (2) simultaneously for d.

Then $t_r = 3 + (r-1)d$ and you substitute the value of d and the required values of r to get the terms.