Answer
$b_1=\dfrac{5}{2}$
$b_2=(\dfrac{5}{2})^2 = \dfrac{25}{4}$
$b_3=(\dfrac{5}{2})^3 =\dfrac{125}{8}$
$b_4=(\dfrac{5}{2})^4 =\dfrac{625}{16}$
The sequence is geometric with a common ratio of $\dfrac{5}{2}$.
Work Step by Step
We need to substitute $1, 2, 3,$ and $4$ for $n$ into the given equation to find the first four terms.
$b_1=(\dfrac{5}{2})^1=\dfrac{5}{2}$
$b_2=(\dfrac{5}{2})^2 = \dfrac{25}{4}$
$b_3=(\dfrac{5}{2})^3 =\dfrac{125}{8}$
$b_4=(\dfrac{5}{2})^4 =\dfrac{625}{16}$
We see that the the next term is equal to $\dfrac{5}{2}$ times the current term and this implies that the sequence is geometric with a common ratio of $\dfrac{5}{2}$.
