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May 6th, 2017, 12:53 AM  #1 
Newbie Joined: May 2017 From: Pakistan Posts: 7 Thanks: 0  A.m a.p g.m g.p
Please solve these 1) Insert n A.Ms between 1 and n² 2) b+c3a/a , c+a3b/b , a+bc/c are in A.P prove that 1/a , 1/b , 1/c are also in A.P 3) If the roots of equation a(bc)x² + b(ca)x + c(ab) = 0 are equal, prove that a, b, c are in H.P. 4) The sums of the first n terms of two A.P.s are in the ratio 3n+31 : 5n3 find the ratio of their nth terms. 5) If G1 and G2 are two G.M.s between b,c and A is their A.M., then show that G1^3 + G2^3 = 2Abc 6) If a,b,c in G.P. and x,y are the A.M.s of a, b and b, c respectively, then prove that a/x + c/y = 2 7) An A.P. has first term of 6 and fifth term of 18 find the sum of the n terms of the progression is greater than 2000 8) Find a G.M. between 3 and 12 9) Sum to n terms the series 2+22+222.... Last edited by skipjack; May 6th, 2017 at 06:44 AM. 
May 6th, 2017, 06:42 AM  #2 
Global Moderator Joined: Dec 2006 Posts: 18,422 Thanks: 1462 
(6). Using b = ar and c = ar², show that 2a/(a + ar) + 2ar²/(ar + ar²) = 2, which is easy to do. (7). n needs to be at least 27. (8). 6 (9). (2/81)(10^(n+1)  9n  10) 