Question

This is the recursive formula for a geometric sequence: f(1) = 8,000 f(n) = 1/2 ⁢f ⁢(n − 1) , for n ≥ 2 what is the fifth term in the sequence? select the correct answer. a. 250 b. 500 c. 1,000 d. 1,600

Answer 1

The recursive formula for this geometric sequence is:

f(1) = 8,000

f(n) = (1/2) * f(n - 1) for n ≥ 2

To find the fifth term (f(5)), you can use the formula recursively:

f(2) = (1/2) * f(1) = (1/2) * 8,000 = 4,000

f(3) = (1/2) * f(2) = (1/2) * 4,000 = 2,000

f(4) = (1/2) * f(3) = (1/2) * 2,000 = 1,000

f(5) = (1/2) * f(4) = (1/2) * 1,000 = 500

So, the fifth term in the sequence is 500, which corresponds to option (b).