Find the missing term in the given series: 6 15 35 ___ 143

Concept

Many number series are built by multiplying together consecutive terms of a fixed reference sequence -- for example, take consecutive prime numbers (2, 3, 5, 7, 11, 13, ...) and multiply each one by the very next prime after it (overlapping pairs, not split into separate non-overlapping groups); this gives a strictly increasing series of semiprimes (numbers that are a product of exactly two primes).

Application

Confirm the rule from the given terms, then apply it to find the missing one:

1. List the primes in order: 2, 3, 5, 7, 11, 13.

2. Pair them consecutively and multiply: 2 x 3 = 6, 3 x 5 = 15, 5 x 7 = 35 -- these match the first three given terms exactly.

3. The next pair in order is 7 x 11, so the missing term = 7 x 11 = 77.

Cross-check

The next pair after that, 11 x 13 = 143, matches the given last term of the series, confirming the rule holds across the whole sequence. 77 is also a semiprime (7 and 11 are both prime), consistent with every other term, so 77 is the missing term.