If 2,7,9,5 are subtracted respectively from four numbers forming a GP , the resulting numbers are in AP , then the smallest of the four numbers is

Step-by-step solution

Let the numbers be a, a r, a r², a r³ . array ll & a-2, a r-7, a r²-9 are in A.P. & a-2+a r²-9=2(a r-7) & a (r²+1 )-11=2 a r-14 & r²+1=2 r- 3 a ...(i) array Further, a r-7+a r³-5=2 (a r²-9 ) a r (r²+1 )-12=2 a r²-18 r²+1=2 r- 6 a r ...(ii) Solving Eqs. (i) and (ii), we get r=2, a=-3 The number are -3,-6-12,-24