Question

Ryan wrote the sequence of numbers below. I , 0.2 , 0.04 , 0.008 , 0.0016 . . . If n stands for the number's position in the sequence, which expression can b used to find the value of any number in the sequence?

Answer 1

The numbers in Ryan's sequence form a geometric sequence, and the expression to find any term is an = 1 × (0.2)^(n-1), where an is the n-th term.

Step-by-step explanation:

The student is working with a geometric sequence, where each term is a certain fraction of the previous term. Ryan's sequence 1, 0.2, 0.04, 0.008, 0.0016, ... can be generated using the formula an = a1 × rn-1, where an is the n-th term of the sequence, a1 is the first term, r is the common ratio, and n is the term's position in the sequence. In Ryan's sequence, the first term a1 is 1, and the common ratio r is 0.2, so the expression to find the value of any number in the sequence is an = 1 × (0.2)n-1.