Question

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

3a + 3a² + 3a³ + . . . + 3an

arithmetic
geometric
both
neither

Answer 1

Option 2 - Geometric series

Explanation:

Given : Series
`3a+3a^2+3a^3+.....+3a^n`

To identify : The following series as arithmetic, geometric, both, or neither.

Solution :

According to the series,

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

If we take 3 common,

`=3(a+a^2+a^3+.....+a^n)`

the above series make is a geometric series as 3 is a constant.

Geometric series is
`\sum_k a_k` where ratio of two terms is
`(a_(k+1))/(a_k)`

In the above given series, the common ratio is a.

As the series satisfy all conditions of geometric series.

Therefore, Option 2 is correct.

Answer 2

The expression 3a + 3a² + 3a³ + . . . + 3an is a geometric expression, because 3 is constant.