Jocelyn Bernard

2022-10-03

A geometric sequence is defined recursively by ${a}_{n}=5{a}_{n-1}$, the first term of the sequence is 0.45. What is the explicit formula for the nth?

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antidootnw

Expert

In a geometric series $\left\{a,ar,a{r}^{2},a{r}^{3},.....\right\}$, a is first term and ratio is r, ${n}^{th}$ term is given by $a{r}^{n-1}$. Note $r=\frac{{a}_{m}}{{a}_{m-1}}$ or ${a}_{m}=r{a}_{m-1}$
As ${a}_{n}=5{a}_{n-1}$, r=5 and first term a=0.45
Hence, ${n}^{th}$ term is given by $0.45×{5}^{n-1}$

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