Determine whether the sequence 80,40,20,10,5,... is arithmetic and if it is, what is the common difference

gasavasiv

gasavasiv

Answered question

2022-10-16

Determine whether the sequence 80,40,20,10,5,... is arithmetic and if it is, what is the common difference

Answer & Explanation

Momellaxi

Momellaxi

Beginner2022-10-17Added 14 answers

To find if a sequence is arithmwtic, geometric or neither you have to check if either the difference (arithmetic sequence) or quotient (geometric sequence) between any 2 consecutive terms is constant.
Arithmetic sequence
a 1 = 80 , a 2 = 40 , a 3 = 20
a 2 - a 1 = 40 - 80 = - 40
a 3 - a 2 = 20 - 40 = - 20
a 3 - a 2 a 2 - a 1 , so the sequence is not arithmetic.
Geometric sequence
40 80 = 20 40 = 10 20 = 5 10 = 0.5
The quotient of 2 consecutive terms is constant 1 2 , so the sequence is geometric.

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