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

Question

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

Tammy Todd 2021-05-12 Answered

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Expert Answer

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.

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