Answered

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write a recursive formula for the sequence 6, 9, 13.5, 20.25,...

Sagot :

Given,

The sequence is 6, 9, 13.5, 20.25,...​

Required

The recursive formula of the sequence.

Here,

First term is 6.

The common ratio between the consecutive terms is,

[tex]\begin{gathered} \frac{9}{6}=1.5 \\ \frac{13.5}{9}=1.5 \\ \frac{20.25}{13.5}=1.5 \end{gathered}[/tex]

So, the recursive formula for the sequence is,

[tex]\begin{gathered} a_n=ar^{n-1} \\ Here,\text{ a = 6, and r = 1.5} \\ a_n=6(1.5)^{n-1} \end{gathered}[/tex]

Hence, the recursive formula is 6(1.5)^(n-1).

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