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: 6400

Step-by-step 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

f (5) = 3200

Step-by-step 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