The nth term of the quadratic sequence is f(n) = 5n² - 7
How to determine the nth term of the quadratic sequence
From the question, we have the following parameters that can be used in our computation:
−2, 13, 38, 73, 118,
A quadratic formula is represented as
f(n) = an² + bn + c
Using the terms and the positions, we have the following system of equations
a(1)² + b(1) + c = -2
a(2)² + b(2) + c = 13
a(3)² + b(3) + c = 38
So, we have
a + b + c = -2
4a + 2b + c = 13
9a + 3b + c = 38
Solving for a, b and c, we have
a = 5, b = 0 and c = -7
Recall that
f(n) = an² + bn + c
Using the above as a guide, we have the following:
f(n) = 5n² + 0n - 7
f(n) = 5n² - 7
Hence, the nth term of the quadratic sequence is f(n) = 5n² - 7