If $U_n = kn^2 + pn$, $U_1 = -1$, $U_5 = 15$, find the values of k and p.

Assessment: WAEC SSCE - Further Mathematics - 2022 (Objective) Subject: Further Mathematics

Question 1 Report

k = -1, p = 2

k = -1, p = -2

k = 1, p = -2

k = 1, p = 2

Answer Details

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