Find the general term for the quadratic sequence with t2=15 , t3=32 , t=90?

Question

I am really struggling with these questions , please show me the complete work for this as I need to find out where I am making sign errors. I get close but can't finish finding a and b and c. I have tried many of these questions , many times and still none work out PLEASE HELP ME!!!!

sorry it should be t5=90

Answer 1

What's a quadratic sequence? Something of the form at^2 + bt + c?

If so, you know

4a+2b+c = 15
9a+3b+c= 30
25a+5b+c=90

Subtracting the second from the third,

16a+2b=60
8a+b=30

Subtracting the first from the second,

5a+b=15

Subtracting one of those from the other, 3a=15. So a = 5.

From there you quickly get b=-10, c = 15.

So the formula is 5t^2-10t+15.