Answer:
[tex]S_{8}[/tex] = - 536
Step-by-step explanation:
The n th term of an arithmetic series is
[tex]a_{n}[/tex] = a₁ + (n - 1)d
where a₁ is the first term and d the common difference
Here a₁ = 10 and [tex]a_{n}[/tex] = - 144 , thus
10 + (n - 1)d = - 144 ( subtract 10 from both sides )
(n - 1)d = - 154
The sum to n terms of an arithmetic series is
[tex]S_{n}[/tex] = [tex]\frac{n}{2}[/tex] [ 2a₁ + (n - 1)d ] , thus
[tex]S_{8}[/tex] = [tex]\frac{8}{2}[/tex] [ (2 × 10) + (- 154) ]
= 4(20 - 154)
= 4 × - 134
= - 536
