Question

How do you tell whether the sequence with the terms `a_3=21, a_5=27, a_12=48` is arithmetic?

Answer 1

It is an arithmetic series. See details below.

Explanation:

In an arithmetic series we can find common difference between two terms `a_m` and `a_n` by using formula `d=(a_n-a_m)/(n-m)`, if common difference is same throughout, we can say this is an arithmetic sequence.

Here we can get three values of `d`

1. `(a_5-a_3)/(5-3)=(27-21)/2=6/2=3`

2. `(a_12-a_5)/(12-5)=(48-27)/7=21/7=3` and

3. `(a_12-a_3)/(12-3)=(48-21)/9=27/3=3`

As we get `d` as constantly same, it is an arithmetic series.