Question

find the numbers are in continued proportion the first term is 5 and the last term is 80 find the numbers.​

Answer 1

Given:

✰ Five numbers are in continued proportion.

✰ The first term is 5 and the last term is 80.

To find:

✠ The numbers.

Solution:

First we will assume that the given numbers which are in continued proportion as a, ak, ak², ak³ and ak⁴ and then we will find the value of the k. We are provided with the first term and the last term, by using this will find the value of k. After that we will substitute the value of k in these numbers to find out all the numbers.

Five numbers are in continued proportion.

Let the continued proportion be:

a, ak, ak², ak³ and ak⁴

➛ First term = 5

➛ a = 5

➛ Last term = 80

➛ ak⁴ = 80

➛ 5 × k⁴ = 80

➛ k⁴ = 80/5

➛ k⁴ = 16

➛ k = ⁴√16

➛ k = 2

Now, find out all the numbers,

➤ a = 5

➤ ak = 5 × 2 = 10

➤ ak² = 5 × 2² = 5 × 4 = 20

➤ ak³ = 5 × 2³ = 5 × 8 = 40

➤ ak⁴ = 5 × 2⁴ = 5 × 16 = 80

∴ The given five numbers in continued proportion are 5, 10, 20, 40 and 80 respectively.

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