Is the following a geometric sequence 3, 9, 27, 81,…

Kasey Reese
2022-10-15
Answered

Is the following a geometric sequence 3, 9, 27, 81,…

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veirenca77

Answered 2022-10-16
Author has **9** answers

A geometric sequence is a sequence of the form

${a}_{0},{a}_{0}r,{a}_{0}{r}^{2},{a}_{0}{r}^{3},...,{a}_{0}{r}^{n},...$

where $a}_{0$ is the first term in the sequence and r is the common ratio between terms.

Looking at the given sequence, we can write it as

$3,3\cdot {3}^{1},3\cdot {3}^{2},3\cdot {3}^{3},...$

which matches the pattern for the first term ${a}_{0}=3$ and common ratio r=3.

${a}_{0},{a}_{0}r,{a}_{0}{r}^{2},{a}_{0}{r}^{3},...,{a}_{0}{r}^{n},...$

where $a}_{0$ is the first term in the sequence and r is the common ratio between terms.

Looking at the given sequence, we can write it as

$3,3\cdot {3}^{1},3\cdot {3}^{2},3\cdot {3}^{3},...$

which matches the pattern for the first term ${a}_{0}=3$ and common ratio r=3.

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