In a G.P., `a = 1, r = -2/3,S_n = (55)/(81)`, find n.

If {a_n} is a G.P. and a_1=4 ,r=5, find a_6 and S_6 .

Given a G.P. with a= 1, r= sqrt2 . Find S_20 .

Find the indicated term(s) of the following A.P.' s : a= 1/5, d= 2/3 ,a_18, a_n .

If S_1,S_2,S_3 be the sum of n, 2n, 3n terms of a G.P., show that : S_1(S_3-S_2)= (S_2-S_1)^2 .

If the (m+1)t h ,(n+1)t h ,a n d(r+1)t h terms of an A.P., are in G.P. and m ,n ,r are in H.P., then find the value of the ratio of the common difference to the first term of the A.P.

If a ,a_1, a_2, a_3, a_(2n),b are in A.P. and a ,g_1,g_2,g_3, ,g_(2n),b . are in G.P. and h s the H.M. of aa n db , then prove that (a_1+a_(2n))/(g_1g_(2n))+(a_2+a_(2n-1))/(g_1g_(2n-1))++(a_n+a_(n+1))/(g_ng_(n+1))=(2n)/h

If in an A.P. S_1=6 and S_7=105 , prove that : S_(n),S_(n-3)::(n+3),(n-3) .

Determine the number n of terms of the G.P. 3,6,12, .......... so that S_n = 381 .

lf n! , 3xxn! and (n+1)! are in G P, then n!, 5 x n! and (n+1)! are in

If a,b,c,d are in G.P., prove that (a^(n) + b^(n)), (b^(n) + c^(n)), (c^(n) + d^(n)) are in G.P.