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

Answer 1

The correct option is A 5,8,12

Given $a,b,c$ are three numbers between 2 and 18 and $a+b+c=25$ ...(i)
2,a,b are consecutive terms of A.P, then
so we can write , $a=\frac{(b+2)}{2}$...(ii)
also given b,c,18 are consecutive terms of a GP
so 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 $c=12$