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

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