# Probably member

Look at the series
2,6,25,96,285, ?
What number should come next?

Result

a5 =  568

#### Solution:

$\ \\ a_{ 0 } = 2 \ \\ a_{ 1 } = a_{ 0 } \cdot \ 6-6 = 2 \cdot \ 6-6 = 6 \ \\ a_{ 2 } = a_{ 1 } \cdot \ 5-5 = 6 \cdot \ 5-5 = 25 \ \\ a_{ 3 } = a_{ 2 } \cdot \ 4-4 = 25 \cdot \ 4-4 = 96 \ \\ a_{ 4 } = a_{ 3 } \cdot \ 3-3 = 96 \cdot \ 3-3 = 285 \ \\ a_{ 5 } = a_{ 4 } \cdot \ 2-2 = 285 \cdot \ 2-2 = 568$

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