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

rakesh05 | High School Teacher | (Level 1) Assistant Educator

Posted on

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`

justaguide | College Teacher | (Level 2) Distinguished Educator

Posted on

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