Ques : Find 4 numbers in GP in which the sum of the extreme terms is 112 and the sum of the middle terms is 48. Share with your friends Share 0 Neha Sethi answered this Dear student Let the four terms be a,ar,ar2 and ar3 respectively.A.T.Qa+ar3=112 ...1ar+ar2=48 ....2Dividing eq 1 by eq2, we geta+ar3ar+ar2=112481+r3r+r2=73⇒3+3r3=7r+7r2⇒3r3-7r2-7r+3=0Also, -1 is a root . So, r+1 is a factorNow, r+13r2-10r+3=0⇒r+13r2-9r-r+3=0⇒r+13rr-3-1r-3=0⇒r+13r-1r-3=0⇒r=-1,3,13But r=-1 not possible as 1+r3=0Hence possible values are 13 and 3When r=13Consider ,a+a133=11227a+a27=11228a=3024a=108Thus, numbers are 108,36,12,4When r=3, a+a33=112 27a+a=112⇒28a=112⇒a=4The terms are 4,12,36,108 Regards 4 View Full Answer
