# Math Help - 2 Infinite Geometric Sequence Problems

1. ## 2 Infinite Geometric Sequence Problems

(I think I'm posting in the right place, but not completely sure)
Question 1
The water used in the orchard is stored in a tank.
Each afternoon, 10% of the volume of water in the tank is used.
Each evening, 2 000 litres of water is added to the tank.
This pattern continues each day.
The volume of water, Vn , in the tank on the morning of the nth day is modelled by the difference equation
Vn + 1 = rVn + d where V1 = 45 000 litres.
a. Find r and d.
r =0.9
d =2000
b. In the long term, how many litres of water will be in the tank each morning?

Question 2
A healthy eating and gym program is designed to help football recruits build body weight over an extended period of time. Rob, a new recruit who initially weighs 73.4 kg, decides to follow the program.
In the ﬁrst week he gains 400 g in body weight.
In the second week he gains 380 g in body weight.
In the third week he gains 361 g in body weight.
If Rob continues to follow this program indeﬁnitely, and this pattern of weight gain remains the same, his eventual body weight will be closest to
A. 74.5 kg
B. 77.1 kg
C. 77.3 kg
D. 80.0 kg
E. 81.4 kg

I tried S(infinity)=a/(1-r) But it can up with some crazy answer which couldn't be right.
Any help would be greatly appriciated.

2. Q1 b) The quantity of liquid will stabilise when 10% of the amount Vn used in the afternoons becomes equal to 2000 liters added in the evenings.

3. Question 2

In week 1 he gains 400g, in week 2 he gains 380g so in week x he will gain 400-(20-(week-1))g.
When he has reached a stable weight, add the weigh gained to the original and there is your answer.

4. Q2.

If the pattern goes like this
+400
+(400-20)
+(400-(20+19))
+(400-(20+19+18))+...
.
.
+(400-(20+19+18+...+1))

Then after 21 weeks the mass gained weekly would remain constant 400-(20*21)/2=190g, and after that every week he would put on additional 190g so he
continues with this program indefinitely he'd explode?

Am I mistaking somewhere?

5. Code:
week    Gain(g)

1    400
2    380    20
3    361    19
4    343    18
5    326    17
6    310    16
7    295    15
8    281    14
9    268    13
10    256    12
11    245    11
12    235    10
13    226    9
14    218    8
15    211    7
16    205    6
17    200    5
18    196    4
19    193    3
20    191    2
21    190    1
22    190    0
Not sure if this helps - we may both be wrong!