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?

antidootnw

Beginner2022-10-04Added 10 answers

In a geometric series $\{a,ar,a{r}^{2},a{r}^{3},.....\}$, 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 $0.45\times {5}^{n-1}$

As $a}_{n}=5{a}_{n-1$, r=5 and first term a=0.45

Hence, $n}^{th$ term is given by $0.45\times {5}^{n-1}$

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