find three nos. a,b,c between 2 and 18 such that (1)their sum is 25 (2)nos.2,b,c are consecutive terms of A.P. (3)b,c,18 are consecutive terms of G.P.

1

answer:3,9,13

2

answer:2,4,6

3 answer:2,6,18

Hi

Let the sequence be 2,a,b,c,18

Given that a+b+c=25-----(1)

As 2,b,c are in A.P, 2b=2+c----(2)

so b=(c+2)/2

Put this in 1st eq.

So 2a+3c=48---(3)

Now consider 2,b,c

Their sum= (n/2)((2)(2)+(n-1)(d))

Here, n=no of terms=3

d=Common difference of A.P

so 25=(9+d)/2

Now d=16/3.

That means b=2+d=2+(16/3)=22/3

c=b+d=22/3 + 16/3 = 38/3

From eq(1), a+b+c=25

Put values of b&c.

We get a=5

And you can find that all the given conditions are satisfied.

Hope its clear.