Related InterviewSolutions

• If `a ,b ,c`are in G.P., then prove that `loga^n ,logb^n ,logc^n`are in A.P.
• If `a ,b ,c ,d`are in A.P. and `x , y , z`are in G.P., then show that `x^(b-c)doty^(c-a)dotz^(a-b)=1.`
• If `a ,b ,c`are three distinct real numbers in G.P. and `a+b+c=x b ,`then prove that either x < -1 or x > 3
• If `a ,b ,c ,d`are in G.P. prove that:`(a^2+b^2),(b^2+c^2),(c^2+d^2)`are inG.P.`(a^2-b^2),(b^2-c^2),(c^2-d^2)`are inG.P.`1/(a^2+b^2),1/(b^2+c^2),1/(c^2+d^2)`are inG.P.`(a^2+b^2+c^2),(a b+b c+c d),(b^2+c^2+d^2)`
• Let `x`be the arithmetic mean and `y ,z`be tow geometric means between any two positive numbers. Then, prove that`(y^3+z^3)/(x y z)=2.`
• If the A.M. of two positive numbers `aa n db(a > b)`is twice their geometric mean. Prove that : `a : b=(2+sqrt(3)):(2-sqrt(3))dot`
• In a finite G.P. the product of the terms equidistant from thebeginning and the end is always same and equal to the product of first andlast term.
• Sum the series : `x(x+y)+x^2(x^2+y^2)+x^3(x^3+y^3+ ton`terms.
• The `(m+n)t ha n d(m-n)t h`terms fa G.P. ae `pa n dq`respectively. Show that the mth and nth terms are `sqrt(p q)a n dp(q/p)^(m//2n)`respectively.
• In a G.P. of positive terms if any terms is equal to the sum of nexttow terms, find the common ratio of the G.P.