If Un = kn\(^2\) + pn, U\(_1\) = -1, U\(_5\) = 15, find the values
FURTHER MATHEMATICS
WAEC 2022
If Un = kn\(^2\) + pn, U\(_1\) = -1, U\(_5\) = 15, find the values of k and p.
- A. k = -1, p = 2
- B. k = -1, p = -2
- C. k = 1, p = -2
- D. k = 1, p = 2
Correct Answer: C. k = 1, p = -2
Explanation
Un = kn\(^2\) + pn,
U\(_1\) = -1,
U\(_5\) = 15,
when n = 1
U1 = k(1)\(^2\)+ p(1) = -1
k + p = -1 --------eqn1
when n = 5
U\(_5\) = k(5)\(^2\)+ p(5) = 15
25k + 5p = 15 --------eqn2
multiply eqn1 by 5 and eqn2 by 1
5k + 5p = -5 -------eqn3
25k + 5p = 15 -------eqn4
eqn4 - eqn3
20k = 20
k = 1
sub for k in eqn1
1 + p = -1
p = -1 -1 = -2
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