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A bizarre sequence (Posted on 2003-07-28) Difficulty: 4 of 5
Here's a sequence:

2, 4, 8, 13, 20, 29, _, _.

What numbers go into the blanks, and what is the rule for the sequence?

See The Solution Submitted by Lewis    
Rating: 3.5000 (4 votes)

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Solution Puzzle Solution Comment 14 of 14 |
(In reply to Answer by K Sengupta)

Let the pth term of the sequence be S(p).
Then, S(p) = F(p) + T(p), where:
F(p) = pth term of the Fibonacci Sequence


T(p) = pth triangular number
We thus set up the following table:
p   F(p)   T(p)    S(p)
1    1       1      2 
2    1       3      4
3    2       6      8 
4    3      10     13
 
5    5      15     20
6    8      21     29
7    13     28     41
8    21     36     57

Accordingly, S(7) = 41, S(8) = 57, and consequently:
The required numbers that go into the blanks are 41 
and 57.

Edited on April 1, 2008, 12:26 pm
  Posted by K Sengupta on 2008-04-01 12:26:14

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