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What number follows in this series, 23, 3, 18, 9, 13, 27, 8, ?

User Pat Hensel
by
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1 Answer

10 votes

Answer:

81

Step-by-step explanation:

This pattern is a complex pattern where there are two different patterns happening. It is similar to the following:

0, 10, 0, 9, 0, 8, 0, 7, 0, 6, 0, 5, 0, 4, 0...

Note that in the pattern I've written, starting with the first term, every other number is exactly zero, so I can deduce that two terms after the last given term, it will be a zero.

Also, beginning with the second term, every other term decreases by 1. So, the next term in the pattern I've written would be 3, because 4-1 = 3.

For your given pattern, 23, 3 18, 9, 13, 27, 8, __ ...

Note that beginning with the first term, and looking only at every other term, the terms are decreasing by 5. (23-18 = 5, 18-13 = 5, 13-8 = 5.)

Beginning with the second term, and looking only at every other term from there, the terms are increasing, but at a changing rate (changing from 3 to 9 is a difference of 6, but from 9 to 27 is a difference of 18). This pattern is geometric, and the terms are multiplied by 3 (note that the quotient 9/3 = 3, and 27/9 = 3). So, multiplying the second to last term by 3, we get the next term in the pattern:

27*3 = 81

User Ted Avery
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