Question

What is the sum of the arithmetic series

Answer 1

`S_ {12} = 192`

Explanation:

The nth term of the given arithmetic sequence is

`U_n = 3 + 2n`

The first term of this series is:

`U_1 = 3 + 2(1) = 5`

The last term of this series is when

`n = 12`

`U_ {12}= 3 + 2(12)`

`U_ {12}= 3 + 24 = 27`

The sum of the first n terms of an arithmetic series when the first an last term is known is given by:

`S_n = (n)/(2)(a + l)`

Where a=5 is the first term and l=27 is the last term.

`S_ {12} = (12)/(2)(5 + 27)`

`S_ {12} =6(32) =19 2`