How do you find the answer to missing terms in a sequence if the terms are both ascending and descending?

Question

How do you find the answer to missing terms in a sequence if the terms are both ascending and descending?

Answer 1

In most cases it will be two or more sequences interleaved.

For example:

25 1 22 5 19 9 16 13 13 17 10 21.

breaks down to

25 22 19 16 13 10 combined with

1 5 9 13 17 21

25 1 22 5 19 9 16 13 13 17 10 21.

-24 +21 -17 +14 -10 +7 -3 +0 +4 -7 + 11

We also see that there are 2 sequences of differences:

-24 -17 -10 -3 +4 +11 (differences increasing by 7)

+21 +14 +7 +0 -7 (differences decreasing by 7)

See if the overall sequence can be separated like that,

then analyze each part separately.

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