# If the sum of 3 terms of an arithmetic series is known as 36 is it possible to uniquely define the series?

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justaguide | Certified Educator

The terms of an arithmetic series are defined as Tn = a + (n - 1)*d, where a is the first term and the common difference is d.

If we are given the sum of the first three terms of an arithmetic series as 36, and we take the first term of the series as a and the common difference as d, we get:

a + a+ d + a + 2d = 3a + 3d = 36

=> a + d = 12

It is not possible to define a unique series using this as there are 2 variables a and d and only one equation. We need the sum of at least two groups of terms of the series to find a unique series.

**A unique arithmetic series cannot be defined if we have the sum of the first three terms of an arithmetic series.**