what will be the next number for the series 8,10,18,44,128

Question

how can we find the answer for this series,its a number series.

Answer 1

The following formula fits the series: a_n=7n⁴/6-5n³+59n²/6-4n+8, where a_n is the term for n≥0.

So a₀=8, a₁=10, a₂=18, a₃=44, a₄=128, a₅=338. Therefore, the next term is 338 according to this formula.

By the formula a₃ should be (n=3):

7×81/6-5×27+59×9/6-12+8=189/2-135+177/2-4=183-139=44 which matches a₃ from the actual series.

Other formulas may apply. More terms would be needed to confirm the derived formula.