# How do you tell whether the sequence 1, 2, 4, 7, 11 is arithmetic?

Mar 31, 2017

It is not an arithmetic sequence.

#### Explanation:

In an arithmetic sequence, the difference between a term and its immediately preceding term is always same.

Let use see here,

$2 - 1 = 1$

$4 - 2 = 2$

$7 - 4 = 3$

$11 - 7 = 4$

Here the difference is continuously increasing

Hence, it is not an arithmetic sequence.

Note: In an geometric sequence, the ratio of a term to its immediately preceding term is always same. This is not the case here as $\frac{2}{1} = 2$, $\frac{4}{2} = 2$ but $\frac{7}{4} \ne 2$ and $\frac{11}{7} \ne 2$. Hence, it is not a geometric sequence too