Given:
The sequence is:
2, 6, 10, 15,...
To find:
Whether the given sequence is Arithmetic, Geometric, Neither.
Solution:
We have,
2, 6, 10, 15,...
Different between consecutive terms are:
[tex]6-2=4[/tex]
[tex]10-6=4[/tex]
[tex]15-10=5[/tex]
Since [tex]4\neq 5[/tex], therefore the given sequence has no common difference. It means it is not an arithmetic sequence.
Ratio of consecutive terms are:
[tex]\dfrac{6}{2}=3[/tex]
[tex]\dfrac{10}{6}=\dfrac{5}{3}[/tex]
Since [tex]3\neq \dfrac{5}{3}[/tex], therefore the given sequence has no common ratio. It means it is not a geometric sequence.
Since the given sequence is neither arithmetic nor geometric, therefore the correct option is C.
