Question

Evaluate the partial sum 9+12+15...+51+54+57

Answer 1

The partial sum is 561

Explanation:

Given:

The arithmetic series = 9+12+15...+51+54+57

Partial sum between 9 and 57, with d=3

To Find :

The partial sum = ?

Solution

The given series is a arithmetic series with difference 3.

So the series is

9,12,15,18,21,24,27,30,33,36,29,42,45,48,52,51,54,57

Thus There are 17 terms,

Here the is a middle term is the the ninth,

The 9 term is

`a_ 9 = a_0 +(n-1)d`

`a_ 9 = 9 +(9-1)3`

`a_ 9 = 9 +(8)3`

`a _9 = 33`

Now the

The partial sum is 33 x 17 = 561