If m arithmetic means and three geometric means are inserted between 3 and 243 such that 4th A.M, is equal to 2nd G.M, then m is equal to________

Suppose that 3,x1,x2,x3,…,xm,243 are in arithmetic progression and 3,a,b,c,243 are in geometric  progression with common ratio 1Therefore,243=3r4r=3b=3r2=27Given that x4=b3+4d=27d=6Hence, 243=3+m+16m+1=243−36=40m=39