Question

Which statements are true for the given geometric sequence? Check all that apply.

The domain is the set of natural numbers.
The range is the set of natural numbers.
The recursive formula representing the sequence is f(x + 1) = Three-halves(f(x )) when f(1) = 4.
An explicit formula representing the sequence is
f(x) = 4(three-halves) Superscript x
The sequence shows exponential growth.

Answer 1

True
- The domain is the set of natural numbers. (Sequences are indexed by n = 1,2,3,... here.)
- The recursive formula f(x+1) = (3/2)·f(x) with f(1)=4. (Multiplying by the common ratio 3/2 gives the next term.)
- The sequence shows exponential growth. (Common ratio > 1.)

False
- The range is the set of natural numbers. (Terms become non-integers like 13.5, so the range is not all natural numbers.)
- The explicit formula f(x) = 4(3/2)^x. (With f(1)=4 the correct explicit form is f(x) = 4(3/2)^(x−1).)