Litzy Wallace

2022-03-27

Define whether sequence is arithmetic or geometric and write the n-th term formula
1) $11,17,23,\dots$
2) $5,15,45,\dots$

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Expert

(1) $11,17,23,\dots$
$17-11=6$, $23-17=6$, thus, $r=6$ and the sequence is arithmetic
n-th term: $a+\left(n-1\right)d$
$=11+\left(n-1\right)6$
$=11+6n-6$
$=6n+5$ (n-th term formula)
(2) $5,15,45,\dots$
$\frac{15}{5}=3$ and $\frac{45}{15}=3$, thus, $r=3$ and the sequence is geometric
n-th term: $a{r}^{n-1}$
$=5×{3}^{n-1}$ (n-th term formula)

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