Check whether the following numbers are in continued proportion.i. 2,

1.	Check whether the following numbers are in continued proportion.i. 2, 4, 8 ii. 1, 2, 3 iii. 9, 12, 16iv. 3, 5, 8
Answer» If a, b, c are in continued proportion then b² = ac. i. 2, 4, 8 Let, a = 2, b = 4 and c = 8 Here, b² = 4² = 16 ac = 2 x 8 = 16 ∴ b² = ac ∴ 2, 4,8 are in continued proportion. ii. 1, 2, 3 Let, a = 1, b = 2 and c = 3 Here, b² = 2² = 4 ac = 1 x 3 = 3 ∴ b² ≠ ac ∴ 1, 2,3 are not in continued proportion. iii. 9, 12, 16 Let, a = 9, b = 12 and c = 16 Here, b² = 12² = 144 ac = 9 x 16 = 144 ∴ b² = ac ∴ 9, 12, 16 are in continued proportion. iv. 3, 5, 8 Let, a = 3, b = 5 and c = 8 Here, b² = 5² = 25 ac = 3 x 8 = 24 ∴ b² ≠ ac ∴ 3, 5, 8 are not in continued proportion.

Check whether the following numbers are in continued proportion.i. 2, 4, 8 ii. 1, 2, 3 iii. 9, 12, 16iv. 3, 5, 8

Answer»

If a, b, c are in continued proportion then

b² = ac.

i. 2, 4, 8

Let, a = 2, b = 4 and c = 8

Here, b² = 4² = 16

ac = 2 x 8 = 16

∴ b² = ac

∴ 2, 4,8 are in continued proportion.

ii. 1, 2, 3

Let, a = 1, b = 2 and c = 3

Here, b² = 2² = 4

ac = 1 x 3 = 3

∴ b² ≠ ac

∴ 1, 2,3 are not in continued proportion.

iii. 9, 12, 16

Let, a = 9, b = 12 and c = 16

Here, b² = 12² = 144

ac = 9 x 16 = 144

∴ b² = ac

∴ 9, 12, 16 are in continued proportion.

iv. 3, 5, 8

Let, a = 3, b = 5 and c = 8

Here, b² = 5² = 25

ac = 3 x 8 = 24

∴ b² ≠ ac

∴ 3, 5, 8 are not in continued proportion.