Question

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

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, $d_1\neq d_2$, therefore the given sequence have no common difference between consecutive terms.

So, the given sequence is not arithmetic.

Therefore, the correct option is c.