Question

Help please!

0, 7, 18, 33, 52
Write an explicit expression that can be used to find the nth term of the sequence above.What is the 18th term of the sequence?

Answer 1

2n^2+n-3, 663

Explanation:

Answer 2

2n^2+n-3, 663

Explanation:

This is the same as having (1, 0), (2, 7), (3, 18), (4, 33), (5, 52)

We know that this is a parabola because the difference of the differences is a constant:

7, 11, 15, 19

4, 4, 4

this means the nth term is an^2+bn+c

we know a = 2 because the 2a is the difference's difference of 4, 4/2 = 2

now we plug in points to find the others:

2*1^2 + b*1 + c = 0 = 2 + b + c

so b + c = -2

2*2^2 + b*2 + c = 7 = 8 + 2b + c

so 2b + c = -1

2b + c - (b + c) = -1 - - 2 = b = 1

so b = 1

b + c = -2 = 1 + c

c = -3

we put these together to get our answer

2n^2 + n - 3

for 18 this is 2 * 18^2 + 18 - 3 = 663