Question

# Find the three numbers a,b,c between 2 and 18 such that (I) their sum in 25 (II) the numbers 2, a, b are consecutive terms of an AP (III) the numbers b,c,18 are consecutive terms of a GP.

A
5,8,12
B
5,8,10
C
8,10,12
D
4,5,8

Solution

## The correct option is A 5,8,12Given $$a,b,c$$ are three numbers between 2 and 18 and $$a+b+c=25$$ ...(i)2,a,b are consecutive terms of A.P, thenso we can write , $$a\;=\;\frac{(b\;+\;2)}{2}$$...(ii)also given b,c,18 are consecutive terms of a GPso it implies $$c^2\;=\;18b$$...(iii)From equations (i), (ii) and (iii), we get $$b=8$$ and $$32$$ , since $$b$$ is between 2 and 18 , therefore taking $$b = 8$$and then taking the value of b and putting it in other 2 equations we get the values of $$a\;=\;5$$  and  $$c\;=\;12$$Maths

Suggest Corrections

0

Similar questions
View More

People also searched for
View More