# The steps to prove whether a given number sequence is an arithmetic progression

The steps to prove whether a given number sequence is an arithmetic progression.

Step 1: List down any three consecutive terms. [Example: ${T}_{1},{T}_{2},{T}_{3}$ .]
Step 2: Calculate the values of ${T}_{3}-{T}_{2}$  and ${T}_{2}-{T}_{1}$ .
Step 3: If ${T}_{3}-{T}_{2}={T}_{2}-{T}_{1}=d$ , then the number sequence is an arithmetic progression.

[Try Question 8 and 9 in SPM Practice 1 (Arithmetic Progression)]

Example :

Prove whether the following number sequence is an arithmetic progression
(a) 7, 10, 13,....
(b) -20, -15, -9 ,......