If the 12th term of an arithmetic progression is seven times the 2nd term and the 8th term is three
more than ten times of the first term. If the first term and common ratio of an geometric
progression is equal to first term and common difference of the arithmetic progression
respectively, then find the 5th term of the geometric progression.

Let the first term of the ap be a and the common difference be dNow ,Atqa+11d=7(a+d)=>6a=4d=>a=2/3dAgain we havea+7d=10*a +3on putting a=2/3d and solving we get d=3 so a=2as first term of the ap is equal to the first term of the gp and common difference of the ap is equal to the common ratio of the gp So we have,a=2 and r=3Now 5th term of the gp=ar^4=2*3^4=2*81=162therefore the fifth term of the ap is 162.