Finding the Next Value in a Sequence:
More Non-Mathematical "Sequences"
(page 7 of 7)

Sections: Common differences, Recursions, General examples, Non-math "sequences"

• Find the next number in the sequence:  6, 6, 7, 9, ...

"Sunday" is spelled with six letters.
"Monday" is spelled with six letters.
"Tuesday" is spelled with seven letters.
"Wednesday" is spelled with nine letters.

• Find the next term in the sequence:
F21, S23, T25, T27, S29, M31.
• F21: Friday the 21st.
S23: Sunday the 23rd.
T25: Tuesday the 25th.
T27: Thursday the 27th.
S29: Saturday the 29th.
M31: Monday the 31st.

Skipping every other day, the next term must be "Wednesday the 2nd", or "W2" (or maybe "W02").

(If you're not sure about this, then pull out a calendar and find a month where Friday falls on the twenty-first. See where this leads you.)

• Find the missing term in the seqence:  325, 446, 567, ___, 709, 820.

Consider the digits for the units, tens, and hundreds places separately:

hundreds digits: 3, 4, 5, ___, 7, 8
tens digits: 2, 4, 6, ___, 0, 2
ones digits: 5, 6, 7, ___, 9, 0

They're adding by one in the hundreds and ones digits, and adding by twos in the tens digit.

The missing term is 688.

• Find the missing term in the sequence: 127863, 12789, ____, 135, 18

Look at the last two digits of the given numbers.

127863:  6 + 3 = 9
12789: 8 + 9 = 17
_______
135: 3 + 5 = 8

Do you see?  They're taking the last two digits, adding them, replacing the last two digits with one zero, and then adding the sum they just found. Completing the pattern:

127863:  6 + 3 = 9:   12780 + 9 = 12789
12789:  8 + 9 = 17:   1270 + 17 = 1287
1287:  8 + 7 = 15:  120 + 15 = 135
135:  3 + 5 = 8:  10 + 8 = 18

The missing number is 1287.

• Given that 1 and 2 yield 9, 3 and 4 yield 20, and 5 and 6 yield 12, find the number after 17 and 12.   Copyright © Elizabeth Stapel 2002-2011 All Rights Reserved

This problem only works in English: Spell the numbers out as words, and count the letters: "one" and "two" each have three letters, and 3×3 = 9. "Three" has five letters and "four" has four; 5×4 = 20. "Five" has four letters and "six" has three; 4×3 = 12. "Seventeen" has nine letters and "twelve" has six, so the missing number is the product of  9 and 6.

• Find the next number in the following sequence: 1, 11, 21, 1211, 111221,....
• This looks like a "math" sequence, but it isn't really. Instead, each term is a description of the preceding term. The first term is just one "1": 11. The second term is two "1's": 21. And so forth:

one 1: 11
two
1's: 21
one
2 and one 1: 1211
one
1, one 2, and two 1's: 111221
three
1's, two 2's, and one 1: 312211

So the next term is "312211".

When given a sequence problem in a math class, you would like to think that it is an actual math problem. So always try first (assuming the sequence is of numbers and not of letters) to find a mathematical rule for it. Try to find a polynomial or exponential formula. If that doesn't work, try to find a recursive relationship. If that doesn't work, you're probably out of luck, but try anyway, and see if you can come up with something clever.

In any case, don't feel that these problems reflect badly on you. These kinds of problems have become trendy, with the philosophy being that you like struggling for days with a math problem that turns out to be non-mathematical, because it broadens your horizons and strengthens your innate love of mathematics and.... Well, they get pretty syrupy and emotional at this point.

Anyway, unless you're explicitly studying sequences and series (in precalulus or calculus), you probably don't have the tools for answering these questions, so you shouldn't take it personally if you're not coming up with the answers.

By the way, I would like to add to the above collection of examples (if they're not already listed on this BrainyPlanet page). If you think you have a good example of a non-mathematical sequence (in particular, a non-math sequence complete with its "answer"), please let me know, and I will consider adding it to this page. Thank you.

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 Cite this article as: Stapel, Elizabeth. "More Non-Mathematical 'Sequences' and Their Answers." Purplemath. Available from http://www.purplemath.com/modules/nextnumb7.htm. Accessed [Date] [Month] 2016

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