Whether the sequence 2,4,8,16,.... is arithmetic, geometric or neither

Darius Nash

Darius Nash

Answered question

2022-09-07

Whether the sequence 2,4,8,16,.... is arithmetic, geometric or neither

Answer & Explanation

empatiji2v

empatiji2v

Beginner2022-09-08Added 18 answers

It is geometric as far as it goes.
Notice that the ratio between each successive pair of terms is constant:
4 2 = 2
8 4 = 2
16 8 = 2
That these ratios are all the same is sufficient for the given terms to form a geometric sequence with general term:
a n = 2 n
The sequence then continues:
2,4,8,16,32,64,128,256,512,1024,2048,...
The question is in the "...". Any finite number of terms does not determine an infinite sequence.
For example we can match the sequence 2,4,8,16 with a cubic polynomial:
a n = 1 3 ( n 3 - 3 n 2 + 8 n )
Then we would find that the next terms would be 30,52,84,...

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