Question

I am giving brainliest, IF WORK IS SHOWN. please help.

Answer 1

Answer:

-2/3

Step-by-step explanation:

The equation of the series:

$a_n = \frac{5-(n-1)}{3} \\a_n = \frac{6-n}{3}$

Where $a_n$ is the nth term and n is the number of terms.

Now let's calculate the partial sum. The equation for the partial sum should be: $S_n = \frac{1}{2}(a_1 +a_n)$

The first term is 5/3.

The 15th term according to our previous equation is:

$a_{15} = \frac{6-15}{3} \\a_{15} = -3$

Put all that together we get:

$S_{15} = \frac{1}{2}(\frac{5}{3}+(-3))\\S_{15} = \frac{5}{6}-\frac{3}{2}\\S_{15} = -\frac{2}{3}$