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Write an exponential equation for the geometric sequence 1, 10, 100, 1000, ... A. an = 10(0.1)n–1 B. an = 10(1)n–1 C. an = 1(10)n–1 D. an = 10(10)n–1

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ANSWER
The exponential equation is

[tex]a_n = 1({10})^{n - 1} [/tex]



EXPLANATION

The given geometric sequence is

[tex]1, 10, 100, 1000, ...[/tex]

The formula for finding the nth term of a geometric sequence is

[tex]a_n = a_1 {r}^{n - 1} [/tex]

where the first term is
[tex]a_1 = 1[/tex]
and the common ratio

[tex]r = \frac{a_2}{a_1} [/tex]

[tex]r = \frac{10}{1} = 10[/tex]
is the ratio between any two consecutive terms of the sequence.


We substitute these values to obtain,
[tex]a_n = 1({10})^{n - 1} [/tex]


The correct answer is C.