Question

Help please!!! Find the sum of the series show your work

Answer 1

`\sum_(i=1)^(12)(3i-1) = 222`

Explanation:

The given series is

`\sum_(i=1)^(12)(3i-1)`

The first term is

`f(1) = 3 * 1 - 1 = 2`

The last term is

`f(12) = 3 * 12 - 1 = 35`

To find the number of terms in the sequence, solve,

`3i - 1 = 35`

`3i = 36 \\ i = 12`

The sum of the first i-terms of an arithmetic sequence is:

`S_i = (i)/(2) (f(1) + f(2))`

We substitute the values to get;

`S_ {12}= (12)/(2) (2+ 35)`

`S_ {12}=6(37)`

`S_ {12}= 222`