Question

Write the explicit formula for the following sequence:12, 18, 27, 40.5, 60.75,

Answer 1

`\text{The explicit formula of the sequence is a}_n\text{ = 12(}(3)/(2))^{n\text{ - 1}}`

Explanation:

Given the below sequence

12, 18, 27, 40.5, 60.75

From the sequence provided, you will see that the sequence is a geometric sequence

The next step is to find the common ratio

`\text{common ratio= }\frac{next\text{ term}}{\text{previous term}}`
`\begin{gathered} \text{Common ratio = }(18)/(12) \\ \text{common ratio = }(3)/(2) \\ \end{gathered}`

Recall that, the nth term of a geometric progression is given as

`a_n=ar^{n\text{ - 1}}`

Where

a = first term

n = number of terms

r = common ratio

The next thing is to find the explicit formula

From the given sequence, the first term of the sequence is 12, and the common ratio of the sequence is 3/2

`\begin{gathered} a_n\text{ = 12 }*(\text{ }(3)/(2))^{n\text{ - 1}} \\ a_n\text{ = 12(}(3)/(2))^{n\text{ - 1}} \end{gathered}`