Which recursive formula can be used to generate the sequence below, where f(1) = 3 and n ≥ 1? 3, –6, 12, –24, 48, … f (n + 1) =

Question

kakasveta

1 month ago

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Which recursive formula can be used to generate the sequence below, where f(1) = 3 and n ≥ 1? 3, –6, 12, –24, 48, … f (n + 1) =

–3 f(n ) f (n + 1) = 3 f(n ) f (n + 1) = –2 f(n ) f (n + 1) = 2 f(n)

Mathematics

2 answers:

tester [12.3K] · Answer 1 · 2026-03-18T19:02:58+03:00

What recursive formula applies to generate the following sequence where f(1) = 3 and n ≥ 1?

3, –6, 12, –24, 48

The applicable recursive formula for this sequence is

f(n + 1) = –2 f(n)

When n=1, f(n) equals 3

Now when n = 2

f(2) = -2 (3) = -6

When n = 3

f(3) = -2 (-6) = 12, and this pattern continues.

AnnZ [12.3K] · Answer 2 · 2026-03-18T19:04:58+03:00

The formula to recursively establish the sequence is:
f(n+1) = -2f(n)

Let's consider an example:
If we set f(n) = 12 to find f(n+1), it should yield -24
Using the formula, the result would be:
f(n+1) = -2*12 = -24.

I hope this is the information you were seeking and that it assists you.