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