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Find the next term in each sequence below, replacing the underscores. Then, replace each of the found integers with the corresponding letter of the alphabet (A = 1, B = 2, etc.). The letters, in order, form a five-letter word.

```128,  64,  32, 16,  8,  4, ___
-3,   0,   3,  6,  9, 12, ___
3,   4,  6,  8, 12, ___
1,   2,   3,  5,  8, 13, ___
110, 109, 105, 96, 80, 55, ___
```

 Submitted by Charlie Rating: 2.4286 (7 votes) Solution: (Hide) ```Descending powers of 2: 2 = B Ascending multiples of 3: 15 = O Primes plus one: 14 = N Fibonacci numbers: 21 = U Subtract successive squares: 19 = S ``` Of course you could fit a fifth degree polynomial to the shown values in the third row along with any value you'd like for the blank. So if you wanted a 7 there, you could seek a polynomial ax^5 + bx^4 + cx^3 + dx^2 + ex + f in which a + b + c + d + e + f = 3 32a + 16b + 8c + 4d + 2e + f = 4 243a + 81b + 27c + 9d + 3e + f = 6 1024a + 256b + 64c + 16d + 4e + f = 8 3125a + 625b + 125c + 25d + 5e + f = 12 7776a + 1296b + 216c + 36d + 6e + f = 7 (say) You'd get -2x^5/15 + 17x^4/8 - 51x^3/4 + 287x^2/8 - 2707x/60 + 23 This was designed to, and does, provide the next term (x=6) of 7. But that would be BOGUS. To get true Extra Value, you need a BONUS. From Page-a-Day, 2008 Mensa 365 Brain Puzzlers calendar. (called that, even though it has a leap-year-day puzzle.)

 Subject Author Date No Subject ed bottemiller 2008-04-14 16:18:22 Value of Problem - re Ay and Dej Mar. brianjn 2008-04-14 06:01:17 Solution Dej Mar 2008-04-14 02:50:56 No Subject bucks 2008-04-14 02:00:06 No Subject Ady TZIDON 2008-04-14 01:38:40 No Subject Ady TZIDON 2008-04-14 01:35:53 Solution? Steve Herman 2008-04-13 12:16:03

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