Enter the first four terms of the sequence

Question

Enter the first four terms of the sequence.

 

f(1) = 2

 and 

f(n) = 2 

·

 f(n − 1) + 4

 for each 

whole number n

 greater than 1.

 

The first four terms of terms of the sequence are: ___, ___, ___, ___,

Answer 1

Assume that f(1)=2 is the first term of the sequence (since it is not explicitly stated), and that the whole numbers are *CONSECUTIVE* whole numbers beginning with 1. Then if f(n)=2*f(n-1)+4 for each whole number n greater than 1, then the remaining three consecutive whole numbers n greater than 1 are 2,3 and 4.

The formula given is recursive, so each solution may be used in calculating the next term:

n=1: f(n)=f(1)=2 (given)

n=2: f(n)=2*f(n-1)+4, or f(2)=2*f(2-1)+4=2*f(1)+4=2*2+4=8

n=3: f(n)=2*f(n-1)+4, or f(3)=2*f(3-1)+4=2*f(2)+4=2*8+4=20

n=4: f(n)=2*f(n-1)+4, or f(4)=2*f(4-1)+4=2*f(3)+4=2*20+4=44

Then the first four terms of the sequence are: 2,8,20,44.