Question

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

Answer 1

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 `2/1=2`, `4/2=2` but `7/4!=2` and `11/7!=2`. Hence, it is not a geometric sequence too