What is the formula for the sequence 2,−1,4,−7,10,−13,16,... ?

Zackary Diaz

Zackary Diaz

Answered question

2022-11-08

What is the formula for the sequence 2 , - 1 , 4 , - 7 , 10 , - 13 , 16 , ... ?

Answer & Explanation

Biardiask3zd

Biardiask3zd

Beginner2022-11-09Added 16 answers

No infinite sequence is determined purely by a finite number of terms, unless you are given further information - e.g. that the sequence is arithmetic or geometric.
That having been said, note that if we multiply the terms of the given sequence by ( - 1 ) n , then we get the sequence:
- 2 , 1 , 4 , 7 , 10 , 13 , 16 , ...
which is (as far as it goes) an arithmetic sequence with initial term −2 and common difference 3.
So a formula that fits the original sequence can be written:
a n = ( - 1 ) n ( - 2 + 3 ( n - 1 ) )

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