Answer:
see explanation
Step-by-step explanation:
(1)
Note the ratio of consecutive terms is common, that is
2000 ÷ 2500 = 0.8
1600 ÷ 2000 = 0.8
1280 ÷ 1600 = 0.8
This indicates that the series is geometric with common ratio r = 0.8
The sum to n terms of a geometric series is
[tex]S_{n}[/tex] = [tex]\frac{a(1-r^n)}{1-r}[/tex] ← a is the first term
Here a = 2500 and r = 0.8, thus
[tex]S_{5}[/tex] = [tex]\frac{2500(1-0.8^5)}{1-0.8}[/tex] = [tex]\frac{2500(0.67232)}{0.2}[/tex] = 8404
(2)
Note the difference in consecutive terms is common, that is
3 - 11 = - 8
- 5 - 3 = - 8
- 13 - (- 5) = - 8
This indicates that the series is arithmetic with common difference d = - 8
The sum to n terms of an arithmetic series is
[tex]S_{n}[/tex] = a₁ + (n - 1)d ← a₁ is the first term
Here a₁ = 11 and d = - 8, thus
[tex]S_{14}[/tex] = 11 + (13 × - 8) = 11 - 104 = - 93
