Answer:
a. geometric
b. an = 2(2)^n-1 or an = 2^n
c. an+1 = an x 2
Step-by-step explanation:
The sequence, 2, 4, 8, 16, 32,...
a. The sequence is geometric because there is a common ratio in the numbers of the sequence. Each number is made by multiplying the common ratio and the previous number.
b. The explicit formula that can be used to find any term is an = 2(2)^n-1 or an = 2^n
Note: the variable n and number 1 is written in italics to show that it should be in subscript
an = a1 (r)n-1
With the common ratio of n being 2 and first number being 2, we have:
an = 2(2)^n-1
or
an = 2^n
c. The recursive formula for the sequence is an+1 = an x 2
an+1 = an x r
Plugging in the values, we have
an+1 = an x 2
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