Question

A geometric sequence is shown below.24, 12, 6, ...Which is the explicit formula for this sequence?

Answer 1

ANSWER

$a_n=24\mleft(\frac{1}{2}\mright)^{n-1}$

EXPLANATION

The generic formula for a geometric sequence is:

$a_n=ar^{n-1}$

a is the first term of the sequence:

$\begin{gathered} a_1=ar^{1-1} \\ a_1=ar^0 \\ a_1=a \end{gathered}$

Therefore, a = 24.

Then, with the second term we can find r:

$\begin{gathered} a_2=24r^{2-1} \\ 12=24r \\ r=\frac{12}{24} \\ r=\frac{1}{2} \end{gathered}$

The explicit formula for this sequence is:

$a_n=24\mleft(\frac{1}{2}\mright)^{n-1}$