Question

NEED ANSWERS AND EXPLANATION ASAP!!!

Answer 1

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

$S_{n}$ = $\frac{a(1-r^n)}{1-r}$ ← a is the first term

Here a = 2500 and r = 0.8, thus

$S_{5}$ = $\frac{2500(1-0.8^5)}{1-0.8}$ = $\frac{2500(0.67232)}{0.2}$ = 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

$S_{n}$ = a₁ + (n - 1)d ← a₁ is the first term

Here a₁ = 11 and d = - 8, thus

$S_{14}$ = 11 + (13 × - 8) = 11 - 104 = - 93