How do you find the common ratio for 1.512, 7.56, 37.8, 189, 945, ...?

May 24, 2018

$\text{common ratio r } = 5$

Explanation:

$\text{a geometric sequence is defined by having a common }$
$\text{ratio (r) between consecutive terms in the sequence}$

$r = {a}_{2} / {a}_{1} = {a}_{3} / {a}_{2} = \ldots \ldots = {a}_{n} / {a}_{n - 1}$

$\text{here } {a}_{2} / {a}_{1} = \frac{7.56}{1.512} = 5$

${a}_{3} / {a}_{2} = \frac{37.8}{7.56} = 5$

${a}_{4} / {a}_{3} = \frac{189}{37.8} = 5$

${a}_{5} / {a}_{4} = \frac{945}{189} = 5$

$\text{common ratio r } = 5$