Question

The sum of three numbers in GP is 63. If we add 1, 18, 8 to these numbers in that order, we obtain an AP. Find the numbers.​

Answer 1

Answer:

The sum of three numbers in G.P. is 56. If we subtract 1, 7, 21 from these numbers in that order, we obtain an arithmetic progression. Find the numbers?

The sum of three numbers in GP is 56. If we subtract 1,7 and 21 from these numbers in that order, we obtain an arithmetic progression. Find the numbers.

Let the numbers in GP be ar,a and ar.

⇒ ar−1,a−7 and ar−21 are in AP.

⇒ar−1+ar−21=2(a−7).

⇒ar+ar−2a=8⋯(1).

The sum of the three numbers in GP is 56.

⇒ar+a+ar=56⋯(2).

From (1) and (2) we get, 3a=48⇒a=16.

Substituting for a in (1), we get, 16r+16r−32=8.

⇒2r+2r−4=1⇒2r2−5r+2=0.

⇒(2r−1)(r−2)=0⇒r=2 or r=12.

⇒ The three numbers are (8,16,32) or (32,16,8).