Question

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

Answer 1

Answer:

Option 2 - Geometric series  

Step-by-step 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 $\frac{a_{k+1}}{a_k}$

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.