Question

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The first four terms of a sequence are shown below:
9, 5, 1, −3
Which of the following functions best defines this sequence?
A.) f(1) = 9, f(n + 1) = f(n) − 4; for n ≥ 1
B.) f(1) = 9, f(n + 1) = f(n) + 4; for n ≥ 1
C.) f(1) = 9, f(n + 1) = f(n) − 5; for n ≥ 1
D.) f(1) = 9, f(n + 1) = f(n) + 5; for n ≥ 1

Answer 1

A.) f(1) = 9, f(n + 1) = f(n) − 4; for n ≥ 1

Explanation:

The first four terms of a sequence are shown below.

Let

f(1) = 9

f(2) = 5

f(3) = 1

f(4) = -3

Therefore we know that

f(2) - f(1) = 5 - 9

f(2) - f(1) = - 4

f(2) = f(1) - 4

f(3) - f(2) = 1 - 5

f(3) - f(2) = - 4

f(3) = f(2) - 4

f(4) - f(3) = -3 - 1

f(4) - f(3) = - 4

f(4) = f(3) - 4

Hence the answer is A.) f(1) = 9, f(n + 1) = f(n) − 4; for n ≥ 1