(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.