Question

Which recursive formula can be used to generate the sequence below, where f(1) = 6 and n ≥ 1?

6, 1, –4, –9, –14, …

f (n + 1) = f(n) + 5
f (n + 1) = f(n) – 5
f (n) = f(n + 1 ) – 5
f (n + 1) = –5f(n)

Answer 1

Hey there! Here's your answer:

f (n + 1) = f(n) - 5

Here's why:

6, 1, –4, –9, –14, ...

We need to analyze our current sequence to know what pattern will follow.

6 - 5 = 1

1 - 5 = -4

-4 - 5 = -9

-9 - 5 = -14

(And So On)

We can see successive terms are found by subtracting 5 from previous terms.

I hope this helps! Have a good day :).