Question

Identify the following series as arithmetic, geometric, both, or neither. 2x + 2x² + 2x³ + . . . + 2xn

Answer 1

The series is an geometric series, terms are generated by multiplying x.

Answer 2

Answer: It is a geometric series.

Explanation:

Since we have given that

`2x+2x^2+2x^3+.............+2x^n`

Here, first term = 2x

Second term = 2x²

So, we can see that there is common ratio, i.e.

`r=(a_2)/(a_1)=(2x^2)/(2x)=x`

Hence, any sequence with common ratio would be geometric series.

Hence, It is a geometric series.