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Andrews [41]
3 years ago
10

NEED ANSWERS AND EXPLANATION ASAP!!!

Mathematics
1 answer:
Elden [556K]3 years ago
7 0

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

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