What is the next number in this sequence: 2, 7, 26, 101, 400, ?

Question

The possible answers are:

 

1595
800
695
1840

1595

800

695

1840

 

Answer 1

Given the sequence

2 7 26 101 400

 

It looks like the relationship between successive number is

 

x_n+1=4x_n-n

 

Where n = 1, 2, 3, 4...

and x_n = 2, 7, 26, 101 400

 

Let's check this.

 

The first number is 2

x₂ = 4(2)-1 = 7

 

The second number is 7

x₃ = 4(7) -2 = 26

 

The third number is 26

x₄ = 4(26) - 3 = 101

 

The fourth number is 101

x₅ = 4(101) - 4 = 400

 

The fifth number is 400

x₆ = 4(400) - 5 = 1595

 

The 6th number should be 1595