# What is the sum of the first 10 terms of the series 2, 6, 10..

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The sum of the first 10 terms of the series 2, 6, 10... has to be determined.

The series 2, 6, 10... is an arithmetic series with the first term 2 and the common ratio 10 - 6 = 6 - 2 = 4.

The sum of n terms of a series is (n/2)*(2a + (n-1)*d)

For the given series the sum of the first 10 terms is (10/2)*(2*2+9*4) = 5*40 = 200

**The required sum of the first 10 terms is 200**

In discuusing the arithmetic series we talk about common difference not the common ratio.

Clearly the terms 2,6,10,.... are terms of an arithmetic series with first term 2 and common difference 4.

The rule to find the sum of `n` terms of an arithmetic series with first term `a` and common difference `d` is given by

`S_n=(n/2)[2a+(n-1)d]` .

Here `n=10` .

`S_10=(10/2)[2.2+(10-1)4]`

`=5[4+9.4]`

`` =`5.40`

**=200. Answer.**