Question

The recursive function for a sequence is given below

What is the 5th term of the sequence?

3,200

6,400

4,800

1,600

Answer 1

1st term of the sequence: f(1)=200, n=1

2nd term of the sequence f(2)
n=2→f(2)=2.f(2-1)=2.f(1)=2.200→f(2)=400

3rd term of the sequence f(3)
n=3→f(3)=2.f(3-1)=2.f(2)=2.400→f(3)=800

4th term of the sequence f(4)
n=4→f(4)=2.f(4-1)=2.f(3)=2.800→f(4)=1,600

5th term of the sequence f(4)
n=5→f(5)=2.f(5-1)=2.f(4)=2.1,600→f(5)=3,200

Answer: First option 3,200

Answer 2

Answer:
3200

Solution:
The value of a term depends on the value of the previous term as shown in the formula. So value of 5th term depends on value of 4th term which itself depends on value of 3rd term which further depends on value of the 2nd term. So we need to find all these values to reach at the 5th term.

f(1) = 200

f(n) = 2 x f(n-1)
So,

f(2) = 2 x f(2-1) = 2 x f(1) = 2 x 200 = 400

f(3) = 2 x f(3-1) = 2 x f(2) = 2 x 400 = 800

f(4) = 2 x f(4-1) = 2 x f(3) = 2 x 800 = 1600

f(5) = 2 x f(5-1) = 2 x f(4) = 2 x 1600 = 3200

So the 5th term of the given recursive function is 3200.