What is the next number in this series:

341, 39, 602, 50, 1003, 64, _______?

(In reply to

answer by K Sengupta)

Let the nth term of the sequence be S(n), and P(n) be the nth prime number.

Then, we observe that:

S(2n-1) = (3n+8)*P(3n+8),

S(2n) = Average (P(3n+9), P(3n+10))

= (1/2)*(P(3n+9) + P(3n+10))

For example, when n=1 and 2 we have:

S(1) = 11*P(11) = 11*31 = 341, since 31 is the 11th prime number.

S(2) = Average(P(12), P(13)) = Average (37, 41) = 39

S(3) = 14*P(14) = 14*43 = 602.

S(4) = Average(P(15), P(16)) = Average (47,53) = 50

We are required to find S(7), so that substituting n=4, we have:

S(7) = 20*S(20) = 20*71 = 1420.

Consequently, the required missing term is 1420.

*Edited on ***May 10, 2008, 4:12 pm**