Answer:
- 1081
Step-by-step explanation:
We require the number of terms in the series.
The n th term of an arithmetic sequence is
[tex]a_{n}[/tex] = a + (n - 1)d
where a is the first term and d the common difference
d = 3 - 8 = - 5 and a = 8, thus
8 - 5(n - 1) = - 102 ← the last term in the series
8 - 5n + 5 = - 102
13 - 5n = - 102 ( subtract 13 from both sides )
- 5n = - 115 ( divide both sides by - 5 )
n = 23 ← number of terms in series
The sum to n terms is calculated as
[tex]S_{n}[/tex] = [tex]\frac{n}{2}[/tex] (first term + last term )
The first term = 8 and the last term = - 102, thus
[tex]S_{23}[/tex] = [tex]\frac{23}{2}[/tex] (8 - 102) = 11.5 × - 94 = - 1081
