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

1 Answer
Mar 9, 2017

Answer:

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.