Can someone please help? Thank you. 1) On her first day in a hospital, Kiri receives u₁ milligrams (mg) of a therapeutic drug. Theamount of the drug Kiri receives increases by the same amount, d, each day. On the seventh day,she receives 21 mg of the drug, and on the eleventh day she receives 29 mg. Kiri receives thedrug for 20 days.Ted is also in a hospital and on his first day he receives a 20 mg antibiotic injection. The amountof the antibiotic Ted receives decreases by 50% each day. On the second day, Ted receives a 10mg antibiotic injection, on the third day he receives 5mg, and so on.a)i) Write down an equation, in terms of u₁ and d, for the amountof the drug that she receives on the seventh day.ii) Write down an equation, in terms of u₁ and d, for the amountof the drug that she receives on the eleventh day.b) Write down the value of d and the value of u₁.c) Calculate the total amount of the drug, in mg, that she receives.d)i) Find the amount of antibiotic, in mg, that Ted receives on the fifthday.ii) The daily amount of antibiotic Ted receives will first be less than0.06 mg on the kth day. Find the value of k.iii) Hence find the total amount of antibiotic, in mg, that Ted receivesduring the first k days.

Introduction to the problem: This questions is the application of Arithmetic Progression(AP). We will be using some standard formulae in order to solve the question. Those are : an=a+n-1d ----1d=an-an-1 ----2 Sn=n2a+(n-1)d2 ------3 Here, a = first term an=nth term Sn= Sum of n terms d= Common difference n= No.of terms here According to the question, u1=First dose (lets take u1 as first term of the AP) d = Common difference Here 'd' is a positive number because the amount of dose is increasing every day. let 'n'= No. of days Part (a): i We need to calculate the amount of drug she receives on 7 th day i.e. a7 here n=7, so, using formula 1, we get, a7=u1+(7-1)da7=u1+6d ------4 (ii) For 11th day,n=11,using formula 1,a11=u1+(11-1)da11=u1+10d -----5Part (b): It is given that a7=21 and a11=29. There equations 4 and 5 become, 21=u1+6d29=u1+10d Solving above equation to get the values of u1 and d. We get, u1=9 and d=2Part (c): Using formula 3 to calculate total amount of drug she received: n=20 a=u1=9d=2 S20=2022(9)+(20-1)2S20=1018+38S20=560 gm Hence she received a total of 560 gm of doses