Question

Identify the following series as arithmetic, geometric, both, or neither.

3a + 3a² + 3a³ + . . . + 3an

arithmetic
geometric
both
neither

Answer 1

It is a Geometric series.

Explanation:

It has a common ratio equal to a:

3a^2 / 3a = a, 3a^3 / 3a^2 = a and so on..

It is a Geometric series.

Answer 2

Answer with explanation:

The given series is:

`3 a + 3 a^2 + 3 a^3 + . . . + 3 a^n`

If you will try out to find out the ratio of

`\rightarrow\frac{\text{Second term}}{\text{First term}} {\text{or}}\frac{\text{Third term}}{\text{Second term}}  {\text{or}} \frac{\text{Fourth term}}{\text{Third term}} ........\\\\ \rightarrow(3a^2)/(3a)=(3a^3)/(3a^2)=(3a^4)/(3a^3)=......=a`

The Ratio of Succeeding term to it's preceding term in the given sequence is constant equal to a.

So, if any Sequence follows this kind of rule or pattern we call it Geometric Progression.

Option B:→ Geometric