Question

What Is the nth term ruld of the quadratic sequence -5,-4,-1,4,11,20,31

Answer 1

-5   - 4    -1    4     11    20    31   subtracting:-
   1       3     5    7      9      11      subtractiing:-    
       2      2     2    2      2

second row is 2 so the rule will contain n^2

so we can write the series as n^2 - 6 , n^2 - 8 , n^2 - 10 etc

the  numbers are in arithmetical sequence with  a1 = 6 and d = -2

so nth term  of our sequence is n^2 - a1 + (n - 1)d = n^2 -2n - 6 + 2
  
  = n^2 - 2n - 4   Answer