Answer:
a. 21 = u1 + 6·d
b. 29 = u1 + 10·d
c. d = 2, u1 = 9
Step-by-step explanation:
a. The given parameters are;
The amount of therapeutic drug Kiri receives on her first at the hospital = u1 milligrams
The amount of drug increase received by Kiri each day = d
The amount of drug Kiri received on the seventh day = 21 mg
The amount of drug she received on the eleventh day = 29 mg
Therefore, we have an arithmetic progression with the formula for the nth term given as follows;
aₙ = a₁ + (n - 1)·d
Where;
a₁ = u1
n = The number of terms
Therefore, for the 7th day, the amount of drugs she receives, which is 21 milligrams, is given as follows;
a₇ = u1 + (7 - 1)·d = u1 + 6·d = 21
The equation for the amount of drugs she receives in terms of u1 and d on the seventh day is given as follows;
21 = u1 + 6·d
b. For the eleventh day, the amount of drugs she receives, which is 29 milligrams, is given as follows;
a₁₁ = u1 + (11 - 1)·d = u1 + 10·d = 29
Therefore, the equation for the amount of drugs she receives in terms of u1 and d on the eleventh day is given as follows;
29 = u1 + 10·d
c. Therefore, we have two equations which are given as follows;
21 = u1 + 6·d................(1)
29 = u1 + 10·d..............(2)
Subtracting equation (1) from equation (2) gives;
29 - 21 = (u1 + 10·d) - (u1 + 6·d)
8 = 4·d
d = 8/4 = 2
d = 2
From equation (1), we have;
21 = u1 + 6·d = u1 + 6×2 = u1 + 12
21 = u1 + 12
21 - 12 = u1
∴ u1 = 9
d = 2, u1 = 9.
