Q. 43.8( 19 Votes )

Check whether the following numbers are in continued proportion.
i. 2, 4, 8

ii. 1, 2, 3

iii. 9, 12, 16

iv. 3, 5, 8

Answer :

(i) Three numbers ‘a’, ‘b’ and ‘c’ are said to be continued proportion if a, b and c are in proportion,


i.e. a:bb:c


or b2 = ac


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


(4)2 = 2 × 8


16 = 16, which holds true.


2, 4, 8 are in continued proportion.


(ii) Three numbers ‘a’, ‘b’ and ‘c’ are said to be continued proportion if a, b and c are in proportion,


i.e. a:bb:c


or b2 = ac


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


(2)2 = 1 × 3


4 = 3, which does not hold true.


1, 2, 3 are not in continued proportion.


(iii) Three numbers ‘a’, ‘b’ and ‘c’ are said to be continued proportion if a, b and c are in proportion,


i.e. a:bb:c


or b2 = ac


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


(12)2 = 9 × 16


144 = 144, which holds true.


9, 12, 16 are in continued proportion.


(iv) Three numbers ‘a’, ‘b’ and ‘c’ are said to be continued proportion if a, b and c are in proportion,


i.e. a:bb:c


or b2 = ac


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


(5)2 = 3 × 8


25 = 24, which does not hold true.


3, 5, 8 are not in continued proportion.


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