Question

Is the following sequence arithmetic? If so, what is the common difference?

1, 2, 4, 8, 16, ...



a. Yes, the common difference is 3.
b. Yes, the common difference is 2.
c. No, the sequence is not arithmetic.
d. Yes, the common difference is - 1.

Answer 1

Given:

The sequence is

1, 2, 4, 8, 16, ...

To find:

Whether the given sequence is arithmetic or not. If yes, then find the common difference.

Solution:

We have,

1, 2, 4, 8, 16, ...

Difference between consecutive terms are

`d_1=a_2-a_1`

`d_1=2-1`

`d_1=1`

Similarly,

`d_2=a_3-a_2`

`d_2=4-2`

`d_2=2`

Since,
`d_1\\eq d_2`, therefore the given sequence have no common difference between consecutive terms.

So, the given sequence is not arithmetic.

Therefore, the correct option is c.