If the vine continues to grow at this rate, it will be. Inches long at the end of 5 weeks
2 answers:
Answer:
The growth at week 5 is 20 inches
Step-by-step explanation:
<em><u>Topic: Arithmetic Progression</u></em>
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;
<u>Method 1</u>
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
<u>Method 1</u>
Between each interval, the vine grows by 4 inches. This is supported by the calculation below
Here, we make use of arithmetic progression formula
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
becomes
Hence, the growth at week 5 is 20 inches
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