# What is the sum of the series 2, 4, 6, 8, 10...48.  I never seem to get the right answer.

The given series is in arithmetic progression.

Here `a_1 = 2`

`d = a_2 - a_1 = 4 - 2 = 2 `

`a_n = 48 `

To find the sum of given numbers, first we need to find how many terms are there in the series. So, we need to find n value.

`a_n = a + (n-1)d `

`48 = 2 + (n-1)2 = 2 + 2n - 2 = 2n `

`therefore n = 48/ 2 = 24 `

Now we need to find sum of 24 terms i.e. `S_24`

`S_n = n/2 ( a_1 + a_n) `

`S_24 = 24/2 (2 + 48) `

`S_24 = 12*50 = 600`

` `

Posted on