Question

What is the nth term of the quadratic sequence: 8,16,26,38,52,68,86?

Answer 1

-8 is the nth term of this sequence

Answer 2

Answer:

$n^{th}\texttt{term}=n^2+5n+2$

Step-by-step explanation:

It is given that the $n^{th}$ term is quadratic

Let us assume $n^{th}$ term as an²+bn+c

When n = 1

        a + b + c = 8 --------------------------eqn 1

When n= 2

        4a + 2b + c = 16 --------------------------eqn 2  

When n= 3

        9a + 3b + c = 26 --------------------------eqn 3

eqn 1 x 4

        4a + 4b + 4c = 32 --------------------------eqn 4

eqn 4 - eqn 2

        2b + 3c = 32 - 16

        2b + 3c = 16 --------------------------eqn 5

eqn 1 x 9

        9a + 9b + 9c = 72 --------------------------eqn 6

eqn 6 - eqn 3

        6b + 8c = 72 - 26

         3b + 4c = 23 --------------------------eqn 7

eqn 5 x 3

         6b + 9 c = 48 --------------------------eqn 8

eqn 7 x 2

          6b + 8c = 46 --------------------------eqn 9

eqn 8 - eqn 9

           c = 48 - 46 = 2

Substituting in eqn 5

           2 b + 3 x 2 = 16

                b = 5

Substituting in eqn 1

           a + 5 + 2 = 8

            a = 1

So

  $n^{th}\texttt{term}=n^2+5n+2$