Question 1153680

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}}}

{{{x[2] = 4(2)-1 = 7}}}
 
The second number is {{{7}}}.

{{{x[3 ]= 4(7) -2 = 26}}}
 
The third number is {{{26}}}.

{{{x[4] = 4(26) - 3 = 101}}}
 
The fourth number is {{{101}}}.

{{{x[5 ]= 4(101) - 4 = 400}}}
 
The fifth number is {{{400}}}.

then,

{{{x[6] = 4(400) - 5 = 1595}}}

answer: {{{1595}}}