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Verified Answer :

Greenleafable

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

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.

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