Question

Select the correct answer.

Select the function that defines the given sequence.
-8, -20, -50, –125, 625,...
ОА
- 1)
f(n) = -8-()
n-
OB.
- 1)
= -8.(29)
OC f(1) = -8
f(n) = f(n − 1), for n = 2, 3, 4, ...
OD. (1) = 8
f(n) = - . 1(n − 1), for n = 2, 3, 4, ...

Answer 1

Option C

Explanation:

f(1) = -8

f(2) = -5/2×-8 = -20

f(3) = -5/2×-20 = -125

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.

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So option C is the answer

Answer 2

C. a1 = -8

an = an-1 * 5/2 for n >1

Explanation:

-8, -20, -50, –125, 625,...

We need to find the common ratio

Take the second term and divide by the first term

-20/-8 = 5/2

Take the third term and divide by the second term

-50/-20 = 5/2

The common ratio is 5/2

A geometric sequence is

an = a1 * r^(n-1)

an = -8 *(5/2)^(n-1)

We can also write a recursive formula

a1 = -8

an = an-1 * 5/2 for n >1