Question

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

Answer 1

Answer:

$\sum_{i=1}^{12}(3i-1) = 222$

Step-by-step explanation:

The given series is

$\sum_{i=1}^{12}(3i-1)$

The first term is

$f(1) = 3 \times 1 - 1 = 2$

The last term is

$f(12) = 3 \times 12 - 1 = 35$

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:

$S_i = \frac{i}{2} (f(1) + f(2))$

We substitute the values to get;

$S_ {12}= \frac{12}{2} (2+ 35)$

$S_ {12}=6(37)$

$S_ {12}= 222$