Question

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

Answer 1

ANSWER
The exponential equation is


`a_n = 1({10})^(n - 1)`



Step-by-step explanation

The given geometric sequence is


`1, 10, 100, 1000, ...`

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


`a_n = a_1 {r}^(n - 1)`

where the first term is

`a_1 = 1`
and the common ratio


`r = (a_2)/(a_1)`


`r = (10)/(1) = 10`
is the ratio between any two consecutive terms of the sequence.


We substitute these values to obtain,

`a_n = 1({10})^(n - 1)`


The correct answer is C.