Question

The recursive function for a sequence is given below.

f(1) = 200
f(n) = 2 · f(n − 1), for n = 2, 3, 4, ...
What is the 5th term of this sequence?

Answer 1

f(5) = 3200

Explanation:

Using the recursive formula to generate the terms, that is

f(2) = 2 × f(1) = 2 × 200 = 400

f(3) = 2 × f(2) = 2 × 400 = 800

f(4) = 2 × f(3) = 2 × 800 = 1600

f(5) = 2 × f(4) = 2 × 1600 = 3200

Answer 2

Answer: 6400

Explanation:

Given :

f(1) = 200

f(n) = 2.f(n-1) , for n = 2 ,3 , 4 , ...

To find the 5th term

when n = 2 , the sequence becomes

f(2) = 2 .f(2-1)

f(2) = 2 f(1)

since f(1) = 200

therefore:

f(2) = 2 x 200

f(2) = 400

When n = 3

f(3) = 2f(2)

f(3) = 2 x 400

f(3) = 800

When n = 4

f(4) = 2 f(3)

f(4) = 1600

When n =5

f(5) = 2f(4)

f(5) = 3200

When n = 6

f(6) = 2f(5)

f(6) = 6400

Since n = 2 , 3 , 4 ... this means that the 5th term if f(6) , therefore ,the 5th term is 6400