Question

Check wether or not the following numbers are in continued proportion.

a) 3,6 and 15
b) 12, 18 and 27

Answer 1

CONTINUED PROPORTION :-

Three numbers are in continued proportion if the middle term is repeated such as;

if 1,2,4 are in continued proportion then it will be

1:2:2:4.

a.) 3,6,15 aren't in continued proportion because 3:6 isn't = 6:15.

b.)12,18,27 is in continued proportion because 12:18 = 18:27.

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Answer 2

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If a, b, c are in continued proportion then

b^2 = ac.

(a) 3,6 and 15

Let, a = 3, b = 6 and c = 15

Here, b^2 = 6^2 = 36

a×c = 3×15 = 45

∴ b2 ≠ ac

∴ It is not in continued proportion .

(b) 12, 18 and 27

Let , a = 12 , b= 18 , c= 27

Here , b^2 = 18^2 = 324

a×c = 12×27 = 324

∴ b2 = ac

∴ It is in continued proportion .