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**