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whats the next three terms in this sequence 3. 2, 5, 10, 50, ___, ___, ___

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2 Answers

Although James has correctly identified one possible answer, this question is in fact ill-posed as the next three terms in the sequence could be any three values.  I'll demonstrate by making the next three terms N1 , N2  and N3.  Then the sequence could be generated as the solutions to this algebraic equation:
 
(x - 2)(x - 5)(x - 10)(x - 50)(x - N1)(x - N2)(x - N3) = 0 where N1 , N2 and N3 are any numbers.
After the first two initial values (2,5), the next value the product of the previous two, or:
 
Fn = Fn-1 x Fn-2
 
10 = 5 x 2
50 = 10 x 5
500 = 50 x 10
25,000 = 500 x 50
12,500,000 = 25,000 x 500
 
 
J.T.