What is the next sequential number?

Question

2,7,26,101,400

Answer 1

Hi Gordon,

 

It looks like the sequence.  The "secret" is to figure out the pattern.  In this case the pattern is based on the following:

 

a_x+1 = 4(a_x)-x

So if we begin with a₁ = 2

 

a₁ = 2

a₂ = 4(2)-1 = 7

a₃ = 4(7) - 2 = 26

a₄ = 4(26) - 3 = 101

a₅ = 4(101) - 4 = 400

a₆ would be the next term

a₆ = 4(400) - 5 = 1595

 

 

 

 

 

Answer 2

Sometimes with sequences you have to "see" a trend before you can describe it. And that, I'm afraid, is the hard part.

 

7 = 4(2) - 1

26 = 4(7) - 2

101 = 4(26) - 3

400 = 4(101) - 4

 

so x(k) = 4x(k-1) - k and that's the recursive version.

 

The next number is 4(400) - 5 = 1595.