Question

What is the next number of the pattern. 2 7 26 101 400

Answer 1

$the\ sequence\ can\ be\ determined\ recursively:\\\\ \left \{ {\big{a_1=2\ \ \ \ \ \ \ \ \ \ \ \ \ \ } \atop\big {a_{n+1}=4\cdot a_n-n}} \right. \\\\\\a_6=4\cdot a_5-5=4\cdot400-4=1600-5=1595\\\\Ans.\ the\ nxt\ term\ is\ 1595.$

Answer 2

2x4-1
7x4-2
26x4-3
101x4-4
400x4-5
and so on . .  
just do the math.