Answer:
Option 2 - Geometric series
Step-by-step explanation:
Given : Series [tex]3a+3a^2+3a^3+.....+3a^n[/tex]
To identify : The following series as arithmetic, geometric, both, or neither.
Solution :
According to the series,
[tex]3a+3a^2+3a^3+.....+3a^n[/tex]
If we take 3 common,
[tex]=3(a+a^2+a^3+.....+a^n)[/tex]
the above series make is a geometric series as 3 is a constant.
Geometric series is [tex]\sum_k a_k[/tex] where ratio of two terms is [tex]\frac{a_{k+1}}{a_k}[/tex]
In the above given series, the common ratio is a.
As the series satisfy all conditions of geometric series.
Therefore, Option 2 is correct.
