What is the pattern in the sequence 1, 1, 0, -1, 0, 7, 28, 79, 192?

Frida Faulkner

Frida Faulkner

Answered question

2022-09-09

What is the pattern in the sequence 1, 1, 0, -1, 0, 7, 28, 79, 192?

Answer & Explanation

darkflamexivcr

darkflamexivcr

Beginner2022-09-10Added 14 answers

Start with the sequence:
1 , 1 , 0 , - 1 , 0 , 7 , 28 , 79 , 192

Form the sequence of differences:
0 , - 1 , - 1 , 1 , 7 , 21 , 52 , 113

Then the sequence of differences of those differences:
- 1 , 0 , 2 , 6 , 14 , 30 , 62

Then the sequence of differences of those differences:
1 , 2 , 4 , 8 , 16 , 32

Subtract this from the original sequence to get:
0 , - 1 , - 4 , - 9 , - 16 , - 25

This is obviously a sequence of negated square numbers.

So a n = 2 n - n 2

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