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

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



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

$r = \frac{a_2}{a_1}$

$r = \frac{10}{1} = 10$
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.