The formula for sum of terms of an AP is
So first find the number of terms:
When you've found you can find the common difference using the formula
Thus the first three terms are
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?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?