Answer:
The growth at week 5 is 20 inches
Step-by-step explanation:
Topic: Arithmetic Progression
Given
From the table,
At Week 1: Total length = 4
At Week 2: Total length = 8
At Week 3: Total length = 12
There are two ways of solving this;
Method 1
Between each interval, the vine grows by 4 inches. This is supported by the calculation below
From week 1 to week 2; 8 - 4 = 4 inches
From week 2 to week 3; 12 - 8 = 4 inches
This means that; the vine will grow by 4 inches to week 4;
Hence, at week 4;
Total length = Week 3 + 4
Total length = 12 + 4 = 16
Similarly, the vine will grow by 4 inches to week 5;
Hence, at week 5
Total length = Week 4 + 4
Total length = 20 + 4 = 24
But this method is not always advisable because it'll be tedious to use for large data; hence the need for method 2
Method 1
Between each interval, the vine grows by 4 inches. This is supported by the calculation below
Here, we make use of arithmetic progression formula
[tex]T_{n} = a + (n - 1)d[/tex]
Take note of the following
a = First term = The growth at first week
a = 4
d = common difference = rate of growth
From week 1 to week 2; the rate of growth is 8 - 4 = 4 inches
From week 2 to week 3; the rate of growth is 12 - 8 = 4 inches
So, d = 4
n = nth term = 5; i.e the 5th week
Tn = the rate of growth at nth week;
In this case, Tn = 5
By substitution
[tex]T_{n} = a + (n - 1)d[/tex] becomes
[tex]T_{5} = 4 + (5 - 1)4[/tex]
[tex]T_{5} = 4 + 4 * 4[/tex]
[tex]T_{5} = 4 + 4 * 4[/tex]
[tex]T_{5} = 20[/tex]
Hence, the growth at week 5 is 20 inches
