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

Question

next three terms in the sequnece 

pattern

Answer 1

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 N_{1 ,} N₂  and N_3.  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.

Answer 2

After the first two initial values (2,5), the next value the product of the previous two, or:

 

F_n = F_n-1 x F_n-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.