Question

Which recursive sequence would produce the sequence 8,-35,137,…?

Answer 1

The recursive sequence that would produce the sequence 8,-35,137,… is T(n + 1) = -3 - 4T(n) where T(1) = 8

How to determine the recursive sequence that would produce the sequence?

The sequence is given as:

8,-35,137,…

From the above sequence, we can see that:

The next term is the product of the current term and -4 added to -3

i.e.

Next term = -3 + Current term * -4

So, we have:

T(n + 1) = -3 + T(n) * -4

Rewrite as:

T(n + 1) = -3 - 4T(n)

Hence, the recursive sequence that would produce the sequence 8,-35,137,… is T(n + 1) = -3 - 4T(n) where T(1) = 8

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