You can see how the difference between two consecutive terms is constantly increasing:
So, for the next terms we'll have to add +9, +11, +13 and so on.
Also, note that is obtained by adding the 2nd odd number to
,
is obtained by adding the 3rd odd number to
, and so on.
So, the recursive formula is
For the explicit formula, recall that the sum of the first n odd numbers is n squared. Taking into account the fact that we're not starting from 1, we have
Answer:
Step-by-step explanation:
First we need to make sure that the leading coefficient is a 1. Ours is a 4, so we need to factor it out, leaving us with
To complete the square, take half the linear term, square it, then add it to both sides. But don't forget about that 4 hanging around out front, refusing to be ignored. Our linear term is 18. Half of 18 is 9, and 9 squared is 81. Add 81 into the parenthesis, but what we REALLY added in was 4*81 which is 324:
To solve this, we need to get the x terms all by themselves. So let's divide both sides by 4 to get
The process of completing the square created a perfect square binomial on the left. We will state this binomial now:
We isolate the x term by taking the square root of both sides:
x - 9 = ±9
From that we have 2 equations:
x - 9 = 9 and x - 9 = -9
Which means that x = 18 or x = 0