Question

If the vine continues to grow at this rate, it will be. Inches long at the end of 5 weeks

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Answer 1

20 inches/ 1ft, 8 inches.

3/12 x 5/x

12 x 5 / 3 = 20

Answer 2

The growth at week 5 is 20 inches

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

`T_(n) = a + (n - 1)d`

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

`T_(n) = a + (n - 1)d` becomes

`T_(5) = 4 + (5 - 1)4`

`T_(5) = 4 + 4 * 4`

`T_(5) = 4 + 4 * 4`

`T_(5) = 20`

Hence, the growth at week 5 is 20 inches