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The Purplemath Forums |
Finding
the Next Value in a Sequence: Sections: Common differences, Recursions, General examples, Non-math "sequences"
"Sunday" is spelled with six letters.
F21: Friday the 21st. 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.)
Consider the digits for the units, tens, and hundreds places separately: hundreds digits: 3, 4, 5, ___, 7, 8
They're adding by one in the hundreds and ones digits, and adding by twos in the tens digit. The missing term is 688.
Look at the last two digits of the given numbers. 127863: 6 + 3 = 9 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 The missing number is 1287.
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.
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 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. << Previous Top | 1 | 2 | 3 | 4 | 5 | 6 | 7 | Return to Index
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