Question

The series 2 + 4 + 8 + 16 + 32 + . . . is:

arithmetic
geometric
both
neither

Answer 1

It's geometric because the numbers increase sequentially by ×4. Arithmetic only change by +/-, geometric by ×/÷

Answer 2

Geometric

Explanation:

We know that,

An arithmetic series has a common difference in successive terms of the series,

While, a geometric series has a common ratio in successive terms of the series,

Given series is,

2 + 4 + 8 + 16 + 32 +..........., so on...

Since, 4 - 2 ≠ 8 - 4 ≠ 16 - 8 ≠ 32 - 16.......

Thus, the given sequence does not have the common difference in successive terms,

Hence, series 2 + 4 + 8 + 16 + 32 +..........., is not an arithmetic series.

Now,

`(4)/(2)=(8)/(4)=(16)/(8)=(32)/(16)....=2`

Thus, the given sequence has a common ratio in the successive terms,

Hence, series 2 + 4 + 8 + 16 + 32 +..........., is a geometric series.

⇒ Second option is correct.