Question

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

Answer 1

`a_n=24\mleft((1)/(2)\mright)^(n-1)`

Step-by-step 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=(12)/(24) \\ r=(1)/(2) \end{gathered}`

The explicit formula for this sequence is:

`a_n=24\mleft((1)/(2)\mright)^(n-1)`