# Thread: How to find terms in a pattern

1. ## How to find terms in a pattern

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?
I understand for the first step you have to find how many terms there are. Through algebra it can be determined there are 20 terms in the sequence, but I don't understand why and if this is application to any question involving arithmetic series. I know the formula and everything, but can I use the formula for every question that's similar to this asking the same question?

2. ## Re: How to find terms in a pattern

The formula for sum of terms of an AP is

$\mathrm{\frac{(no.\ of\ terms) (first\ term + last\ term)}2}$

So first find $n,$ the number of terms: $\frac{n(3 + 136)}2 = 1390.$

When you've found $n,$ you can find the common difference $d$ using the formula $d = \frac{136 - 3}{n-1}$

Thus the first three terms are $3,3+d,3+2d.$