Tammy Todd
2021-05-12
Answered

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

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Macsen Nixon

Answered 2021-05-13
Author has **117** answers

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.

To check if the given sequence is arithmetic, consider first difference. The following is true

Since the first difference is constant it implies that the given sequence is arithmetic.

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