Tell whether the sequence 3,9,27,81,243,... is geometric

racmanovcf

racmanovcf

Answered question

2022-10-13

Tell whether the sequence 3,9,27,81,243,... is geometric

Answer & Explanation

relatatt9

relatatt9

Beginner2022-10-14Added 12 answers

If you think it might be an arithmetic progression, you must be able to find a common difference between each pair of terms. That does not happen here.
Look at the first few pairs:
9−3=6, but 27−9=18 and 81−27=54
The differences you calculate in this way are all different. So, this is not an arithmetic progression.
When you calculate the ratio formed by each pair of consecutive terms, you find:
9 ÷ 3 = 3 , 27 ÷ 9 = 3 , and 81 ÷ 27 = 3
The same ratio appears every time. This is proof that the progression is geometric.
(You will need this common ratio, often symbolized as r, to calculate the nth term or the sum of n terms in the series.)

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