Here's a sequence:
2, 4, 8, 13, 20, 29, _, _.
What numbers go into the blanks, and what is the rule for the sequence?
(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
Puzzle Solution
