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?

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

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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?

$\displaystyle t_n = 136 = 3 + (n-1)d$ .... (1)

$\displaystyle S_n = 1390 =$ 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 $\displaystyle t_r = 3 + (r-1)d$ and you substitute the value of d and the required values of r to get the terms.