Question

Which recursive formula can be used to generate the sequence shown, where f(1) = 5 and n > 1?

5,–1, –7, –13, –19, ...

A) f(n + 1) = f(n) + 6
B) f(n) = f(n +1) – 6
C) f(n +1) = f(n) – 6
D) f(n +1) = –6f(n)

Answer 1

Consider the given sequence,

5, -1, -7, -13, -19, .....

We have to generalize the given sequence using recursive formula.

It is given that f(1)=5.

A) Consider the first recursive formula, f(n+1) = f(n)+6

Let n =1, f(2) = f(1)+6 = 5+6 = 11

This is not the required recursive formula.

B) Consider the second recursive formula, f(n)= f(n+1)-6

Let n =1, f(1) = f(2)-6

5= f(2)-6

f(2)= 11

This is not the required recursive formula.

C) Consider the third recursive formula, f(n+1) = f(n)-6

Let n = 1,

f(2) = f(1)-6 = 5-6 = -1

f(3) = f(2)-6 = -1-6 = -7

f(4)= f(3)-6 = -7-6 = -13

So, this is the required recursive formula for the given sequence.

Option C is the correct answer.