# Let #a_n# be a sequence given by: #{1, 6, 15, 28, 45,66,..., f(n)}#. Show that the generating function #f(n)# is of the form # an^2 + bn + c#. Find the formula by computing the coefficients #a, b, c#?

##### 1 Answer

#### Answer:

#### Explanation:

Strategy:

Take the given sequence find the difference between consecutive numbers:

**Step 1 #rArr# Layer 1**

**Step 2**#rArr# Layer 2, Do it again

Taking the difference is in discrete math is the same as taking the derivative (i.e. slope). took two subtraction (two layers) before we reached a comstant number

Give that I asert that:

All I have to do now find the value of

To solve for

Solving a, b, c using any matrix calculator on the internet:

Check:

PS: You can also use python, I used python simply... It is cool