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Find the nth term of the sequence

2,8,18,32,50


Sagot :

9514 1404 393

Answer:

  an = 2n^2

Step-by-step explanation:

First differences are ...

  8 -2 = 6

  18 -8 = 10

  32 -18 = 14

  50 -32 = 18

And second differences are constant at 4:

  10 -6 = 14 -10 = 18 -14 = 4

This means the sequence can be described by a degree 2 polynomial. The coefficient of the n^2 term is half the second difference: 2. We find nothing else needs to be added to the squared term.

  an = 2·n^2

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