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What is the next number? (Posted on 2005-02-20) Difficulty: 3 of 5
What is the next number in the following series: 17 15 14 13 13 14 17 23 ?

See The Solution Submitted by Swastika Shrivastava    
Rating: 1.2500 (4 votes)

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Solution Puzzle Solution Comment 12 of 12 |
(In reply to answer by K Sengupta)

Let us denote the pth term of the given sequence as S(p). We define:
T(p) = S(p+1) - S(p), and denote the pth term of the Fibonacci Sequence as F(p).

Then, by the given conditions:

T(1) = S(2) - S(1) = 15-17 = -2 = 0-2 = F(0) -2
T(2) = S(3) - S(2) = 14-15 = -1 = 1-2 = F(1) -2
T(3) = -1 = F(2) -2, and so on.

Thus, in general T(p) = F(p-1) - 2.

We know that F(7) = 13, so that:

T(8) = 13-2 = 11

Accordingly, we must have:

S(9) = T(8) + S(8) = 11 + 23 = 34

Consequently, the required next number is 34.


  Posted by K Sengupta on 2008-06-04 00:49:49
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