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Given the sequence 2, 10, 26, 50, 82, ...
We can look at the differences between these numbers:
2 + 8 = 10
10 + 16 = 26
23 + 24 = 50
50 + 32 = 82
and can see that this sequence increments by a value which starts at 2, and itself increments by eight. This means we can describe this sequence with this function:
x
f(x) = 2 + 8∑x
0
f(x) = 2 + 8( x(x + 1) / 2)
f(x) = 2 + 4(x2 + x)
f(x) = 4x2 + 4x + 2
f(x) = 2(2x2 + 2x + 1)
The next value in the sequence then would be:
f(5) = 2(2 * 52 + 2 * 5 + 1)
= 2(50 + 10 + 1)
= 2 * 61
= 122
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