Is the following a geometric sequence 1, -2, 4, -8, 16,…

Hanna Webster

Hanna Webster

Answered question

2022-11-09

Is the following a geometric sequence 1, -2, 4, -8, 16,…

Answer & Explanation

Houston Ochoa

Houston Ochoa

Beginner2022-11-10Added 19 answers

The ratio of any two successive terms listed is −2, so this can be a geometric sequence. I say can be because we do not know what the following terms are.
For example, the same terms are given by the formula:
a n = 1 0 ! - 3 1 ! ( n - 1 ) + 9 2 ! ( n - 1 ) ( n - 2 )
- 27 3 ! ( n - 1 ) ( n - 2 ) ( n - 3 ) + 81 4 ! ( n - 1 ) ( n - 2 ) ( n - 3 ) ( n - 4 )
but this formula would make a 6 = 211 rather than −32
So, the terms listed are consistent with being a geometric sequence with initial term 1 and common ratio −2

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