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, th…

Question

asked Jul 13, 2021 47.1k views

1 Answer

Donn Felker · Answer 1 · 2021-07-16T22:11:26+0000

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.