Question

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

Answer 1

Answer: It is a geometric series.

Step-by-step 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.

$r=\dfrac{a_2}{a_1}=\dfrac{2x^2}{2x}=x$

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

Hence, It is a geometric series.

Answer 2

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