Question

Find the sum of the following arithmetic​ series:

3 +7 +11 +15 +... +47.
The sum of this series is___

Answer 1

The sum of the given series is 300.

Explanation:

Given,

The arithmetic series: 3+7+11+15+.....+47

To find the sum of the series.

Formula

Sum of the series =
`(n)/(2)(a+l)` where, n is the number of term, a is the first term and l is the last term.

nth term of a series =
`a_(n)` = a+(n-1)d where d is the common difference

Now,

Here, a=3

d = 7-3 = 11-7=15-11=4

Hence,

47 = 3+(n-1)4

or, 4(n-1) = 47-3

or, 4(n-1) = 44

or, n-1 = 11

or, n = 12

Now,

Sum =
`(12)/(2)` (3+47) = 300