How to solve an arithmetic sequence
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How to solve an arithmetic sequence

[From: ] [author: ] [Date: 12-05-17] [Hit: ]
25..However, what I cant seem to understand is how to figure it out if the number it increases by switches off (ex. 1........
I've looked it up on Google, and found out how to find missing numbers given a certain arithmetic sequence where numbers are increasing by the same number each time (ex. 5..10..15..20..25..)

However, what I can't seem to understand is how to figure it out if the number it increases by switches off (ex. 1..6..12..17..23..) +5, +6, +5 etc.

So, if a question were to ask, What is the 101st term in the arithmetic sequence 9..15..20..26..31..37..42? How would I solve that?

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What is the 101st term in the arithmetic sequence 9..15..20..26..31..37..42?
Just consider the odd terms.
For odd terms only
nth term = 9+(n-1)*11/2 = (11n+7)/2
101st term = (11*101+7)/2 = 559

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If it alternates, then think of it as a sequence that adds the two alternating guys together.

In your example, you have:

1,6,12,17,...

Observe the subsequence: 1 + (5+6) = 12
12 + (5+6) = 23 etc.
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