Question

Describe the following sequence as arithmetic, geometric or neither.
2, 4, 8, 16, 32. . . .

Answer 1

That is a geometric sequence.

Answer 2

Geometric

Explanation:

Since, a sequence is arithmetic if there is a common difference in the successive terms,

While it is geometric if there is a common ratio in successive terms,

Here, the given sequence,

2, 4, 8, 16, 32..................,

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

⇒ There is not a common difference in successive terms,

Hence, the given sequence is not arithmetic.

Now,

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

⇒ There is a common ratio in successive terms,

Hence, the given sequence is a geometric sequence.