What is the nth term of the quadratic sequence: 6,20,40,66,98,136?

Step-by-step explanation:

Consider the quadratic sequence :  6, 20, 40, 66, 98, 136

A quadratic sequence is of form .

For n = 1 :

   ...(i)

For n = 2 :

   ...(ii)

For  n = 3 :

    ...(iii)

On subtracting equation (ii) from (iii), we get

     ...(iv)

On subtracting equation (i) from (ii), we get

3a+b=14                    ...(v)

On subtracting equation (iv) and (v) , we get

2a=6 which implies a=3

So, from equation (v), we get

From equation (i), we get

c=6-a-b=6-3-5=-2

On putting a = 3 , b = 5, c = -2 in , we get