Divide into pairs. The product of the numbers in each of the three pairs is 6400. But we need to relate the pairs. The first number in each pair is a power of 2: 8=2³, 256=2⁸, 512=2⁹. There is no obvious connection between 3, 8 and 9 and no obvious connection between the members of each pair.
With only three pairs as a guide the expression -2n²+11n-6 could be used to find the power of 2 for the fourth pair. This expression gives 3, 8, 9 for n=1, 2, 3. When n=4, it evaluates as -32+44-6=6, and 2⁶=64, so the next term in the series using this rule is 64, and it’s paired with 100.