Question

*Which of the given numbers are in continued proportion?*

1️⃣ (2,4,8)
2️⃣ (1,2,3)
3️⃣ (6,9,8)
4️⃣ (3,5,8)​

Answer 1

Answer :-

checking all options we get,

→ (2, 4, 8)

→ b² = a * c

→ 4² = 8 * 2

→ 16 = 16

Yes , option (1) is in continued proportion .

→ (1, 2, 3)

→ b² = a * c

→ 2² = 1 * 3

→ 4 ≠ 3

No, option (2) is not in continued proportion .

→ (6, 9, 8)

→ b² = a * c

→ 9² = 6 * 8

→ 81 ≠ 48

No, option (3) is not in continued proportion .

→ (3, 5, 8)

→ b² = a * c

→ 5² = 3 * 8

→ 25 ≠ 24

No option (4) is not in continued proportion .

therefore, only Option (1) is in continued proportion .

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Answer 2

SOLUTION

TO CHOOSE THE CORRECT OPTION

Which of the given numbers are in continued proportion

1. (2,4,8)

2. (1,2,3)

3. (6,9,8)

4. (3,5,8)

CONCEPT TO BE IMPLEMENTED

Three given numbers a, b, c are said to be in continued proportion if

$\sf{a : b = b :c }$

EVALUATION

CHECKING FOR OPTION : 1

Here the given three numbers are 2 , 4 , 8

Now

Ratio of first two Terms

= 2 : 4

= 1 : 2 ( Dividing both terms by 2 )

Ratio of last two Terms

= 4 : 8

= 1 : 2 ( Dividing both terms by 2 )

∴ 2 : 4 = 4 : 8

So 2 , 4 , 8 are in continued proportion

So this option is correct

CHECKING FOR OPTION : 2

Here the given three numbers are 1 , 2 , 3

Now

Ratio of first two Terms

= 1 : 2

Ratio of last two Terms

= 2 : 3

∴ 1 : 2 ≠ 2 : 3

So 2 , 4 , 8 are not in continued proportion

So this option is not correct

CHECKING FOR OPTION : 3

Here the given three numbers are 6 , 9 , 8

Now

Ratio of first two Terms

= 6 : 9

= 2 : 3 ( Dividing both terms by 3 )

Ratio of last two Terms

= 9 : 8

∴ 6 : 9 ≠ 9 : 8

So 6 , 9 , 8 are not in continued proportion

So this option is not correct

CHECKING FOR OPTION : 4

Here the given three numbers are 3 , 5 , 8

Now

Ratio of first two Terms

= 3 : 5

Ratio of last two Terms

= 5 : 8

∴ 3 : 5 ≠ 5 : 8

So 3 , 5 , 8 are not in continued proportion

So this option is not correct

FINAL ANSWER

Hence the correct option is 1. ( 2 , 4 , 8 )

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