Question 971325
2,7,26,101,400,?
<pre>
The recursion formula seems to be:

{{{4*a[n]-n}}}{{{""=""}}}{{{a[n+1]}}}

{{{4*2-1}}}{{{""=""}}}{{{8-1}}}{{{""=""}}}{{{7}}}

{{{4*7-2}}}{{{""=""}}}{{{28-2}}}{{{""=""}}}{{{26}}}

{{{4*26-3}}}{{{""=""}}}{{{104-3}}}{{{""=""}}}{{{101}}}

{{{4*101-4}}}{{{""=""}}}{{{404-4}}}{{{""=""}}}{{{400}}}

{{{4*400-5}}}{{{""=""}}}{{{1600-5}}}{{{""=""}}}{{{1595}}}

Answer: 1595

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</pre>
7,16,8,27,9,?
<pre>
The odd-numbered terms are going 7, 8, 9, 10, ...
The even numbered terms are going 16,27, which is 8*2,9*3,so 10*4

Answer: 10*4 = 40

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</pre>
7,21,8,72,9,?
<pre>
The odd-numbered terms are going 7, 8, 9, 10, ... 
The even-numbered terms are going 7×3¹, 8×3², 9×3³, 10×3&#8309;, ..

Answer:  9×3³ = 9×27 = 243

Edwin</pre>