Question

Five numbers are in continued proportion.The first term is 5 and the last term is 80.Find these numbers.

Answer 1

Continued proportion : Three numbers ‘a’, ‘b’ and ‘c’ are said to be continued proportion if a, b and c are in proportion.
Thus, if a, b and c are in continued-proportion, then
a,b,b,c are in proportion, that means
Product of extremes = Product of means
⇒ a x c = b x b
⇒ a x c = b 2
Continued-proportion is also known as mean proportional .
If ‘b’ is a mean proportional between a and c then b 2 = ac.

Examples :
1) Find the mean proportional between 9 and 25.
Solution :
Let x be the mean proportional between 9 and 25.
⇒ x 2 = 9 x 25
⇒ x 2 = 225
⇒ x = 15
Hence, the mean proportional between 9 and 25 is 15.

Answer 2

Answer:Let the numbers in continued proportion be a,ak,ak raised to2,ak raised to 3,ak raised to 4.

Here a=5 and ak4= 80

Therefore 5×k4=80

Therefore. K4=16

Therefore K=2

Therefore 2 raised to 4 =16

ak=5×2=10. ak raised to 2=5×4=20

ak raised to 3=5×8=40

ak raised to 4=5×16=80

Therefore the numbers are 5,10,20,40,80

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Step-by-step explanation: