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

Expert Answers
rakesh05 eNotes educator| Certified Educator

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.

justaguide eNotes educator| Certified Educator

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