Answer
1. If the difference between adjacent terms is constant for the sequence then the sequence is arithmetic.
2. If the ratio between adjacent terms is constant then the sequence is geometric.
Work Step by Step
A sequence can be determined to be arithmetic or G.P. by the following method.
1. If the difference between adjacent terms is constant for the sequence then the sequence is arithmetic.
2. If the ratio between adjacent terms is constant then the sequence is geometric.
Example- \[1,3,9,27,\ldots \]
In this sequence the difference between the adjacent terms are \[2,7,18\]so this is not an arithmetic sequence.
The ratio between adjacent terms are;
\[\begin{align}
& \frac{3}{1}=3, \\
& \frac{9}{3}=3, \\
& \frac{27}{9}=3
\end{align}\]
which is constant so the given sequence is geometric sequence.
