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
[tex]d_1=a_2-a_1[/tex]
[tex]d_1=2-1[/tex]
[tex]d_1=1[/tex]
Similarly,
[tex]d_2=a_3-a_2[/tex]
[tex]d_2=4-2[/tex]
[tex]d_2=2[/tex]
Since, [tex]d_1\neq d_2[/tex], therefore the given sequence have no common difference between consecutive terms.
So, the given sequence is not arithmetic.
Therefore, the correct option is c.
