Question

A sequence can be generated by using fn = 2f(n-1)+1, where f1 = 4 and n is a whole number greater than 1. What are the first four terms in the sequence?

Answer 1

{9,19,39,79}

Explanation:

Recursive Sequences

The recursive sequence can be identified because each term is given as a function of one or more of the previous terms. Being n an integer greater than 1, then:

f(n) = 2f(n-1)+1

f(1) = 4

To find the first four terms of the sequence, we set n to the values {2,3,4,5}

• For n=2

f(2) = 2f(1)+1

Since f(1)=4:

f(2) = 2*4+1

f(2) = 9

• For n=3

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

Since f(2)=9:

f(3) = 2*9+1

f(3) = 19

• For n=4

f(4) = 2f(3)+1

Since f(3)=19:

f(4) = 2*19+1

f(4) = 39

• For n=5

f(5) = 2f(4)+1

Since f(4)=39:

f(5) = 2*39+1

f(5) = 79