Answer
$a_{7}=100,000$
Work Step by Step
RECALL:
(1) The $n^{th}$ term $a_n$ of a geometric sequence is given by the formula:
$a_n=a_1 \cdot r^{n-1}$
where
$a_1$ = first term
$r$ = common ratio
(2) The common ratio of a geometric sequence is equal to the quotient of any term and the term before it:
$r = \dfrac{a_n}{a_{n-1}}$
The given geometric sequence has $a_1=0.1$.
Solve for the common ratio using the formula in (2) above to obtain:
$r = \dfrac{a_2}{a_1}=\dfrac{1.0}{0.1}=10$
Thus, the $n^{th}$ term of the sequence is given by the formula:
$a_n = 0.1 \cdot (10)^{n-1}$
The 7th term can be found by substituting $7$ for $n$:
$a_{7}=0.1 \cdot (10)^{7-1}
\\a_{7}=0.1 \cdot (10)^6
\\a_{7} = 0.1 \cdot 1000000
\\a_{7}=100,000$
