overrated3245w

2022-09-04

Find the recursive formula... a1=-4 and a4=-500 if given the two terms in a geometric sequence

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Olleschauvh

Expert

In a geometric sequence, if a is the first term and r is the ratio between a term and its preceding term, then ${n}^{th}$ term is given by $a×{r}^{n-1}$.
Here $a={a}_{1}=-4$ and as fourth term is −500
$-4×{r}^{4-1}=-500$ or $4{r}^{3}=500$ or ${r}^{3}=125$ and hence
$r=\sqrt[3]{125}=\sqrt[3]{5×5×5}=5$
Hence recursive formula is ${a}_{1}=-4$ and ${a}_{n+1}=5{a}_{n}$

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