Question

Tell whether the sequence 12, 4, -4, -12, -20, .... is arithmetic. Explain your reasoning.

Answer 1

We know that in arithmetic sequnce the common difference we can calculate
\(d=a_2-a_1=a_3-a_2=...a_n-a_{n-1}\)
To check if the given sequence is arithmetic, consider first difference. The following is true
\(d=a_2-a_1=a_3-a_2=a_4-a_3=a_5-a_4\)
\(-8=4-12=-4-4=-12+4=-20+12\)
Since the first difference is constant it implies that the given sequence is arithmetic.