2,9, 20

Question

1. Determine what kind of growth this is and explain how you know?
2. Explain how you can go about finding an expression for the number of small squares in the nth term.
3. What is the expression for the term of this sequence?

Answer 1

Associate 2,9,20 with (1,2), (2,9), and (3,20)
I can find a quadratic relation of the form y = ax^2 + bx + c

for x=1 : 2 = a + b + c
for x=2 : 9 = 4a + 2b + c
for x=3 : 20 = 9a + 3b + c

subtract the first two: 3a + b = 7
subtract the last two: 5a + b = 11

subtract again: 2a = 4, a = 2
sub into 3a + b = 7 ---> b = 1

sub into original first equation
a+b+c=2
2+1+c = 2 , ----> c = -1

term(n) = 2n^2 + n - 1
for n ≥ 1 , where n is a whole number, this will be always increasing

I don't understand your question for 2.)