Answer:
- 30
Step-by-step explanation:
Note the common difference d between consecutive terms in the sequence
d = 34 - 40 = 28 - 34 = 22 - 22 = - 6
This indicates the sequence is arithmetic with sum to n terms calculated as
[tex]S_{n}[/tex] = [tex]\frac{n}{2}[/tex] [ 2a₁ + (n - 1)d ]
where a₁ is the first term and d the common difference
Here a₁ = 40 and d = - 6, thus
[tex]S_{15}[/tex] = [tex]\frac{15}{2}[/tex] [ (2 × 40) + (14 × - 6) ], that is
[tex]S_{15}[/tex] = 7.5(80 - 84) = 7.5 × - 4 = - 30
