What number is next in this series 2-10-26-50-82?

Answer 1

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