Question

A sequence is defined recursively by the following rules:

f(1) = 3
f(n+1) =2. f(n) – 1
Which of the following statements is true about the sequence? Select all that apply.
A)f(3) = 10
B)f(6) = 66
C)f(5)= 33
D)f(4) = 18
E)f(2) = 5​

Answer 1

• C) f(5)= 33
• E) f(2) = 5​

Explanation:

The recursive definition tells you that values of f(n) will all be odd. (They are one less than an even number.) This observation eliminates all choices except C and E.

The first few values of f(n) are ...

3, 5, 9, 17, 33, 65, ...

From this list, we can see that f(2) = 5 and f(5) = 33, matching choices C and E.

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The explicit formula is ...

`f(n)=2^(n)-1`