Question

How Do You know If A Sequence Is Arithmetic Progression?

Answer 1

To find out if a sequence is Arithmetic Progression or not:

Take any term from the sequence. Subtract the term from its immediate preceding term. If this difference is same for all terms then the sequence is in Arithmetic Progression. The common difference of an Arithmetic Progression (A.P.) is denoted by $d$ and first term of an A.P. is denoted by $a$.

So, a sequence is arithmetic progression if the difference between any two consecutive terms is same.

Example: $2,4,6,8,10,....$

$4-2=2$, $6-4=2$, $8-6=2$, $10-8=2$

The sequence is in Arithmetic Progression and the common difference is $\mathbf{2}$.