Let `a_1 , a_2 ,...` be in harmonic progression with `a_1 = 5` and `a_20 = 25`. The least positive integer n for which `a_n lt 0`

Let a_1 , a_2 , ...., a_100 be an arithmetic progression with a_1 = 3 and S_p = sum_(j = 1)^p a_j , 1 le p le 100 . For any integer n with 1 le n le 20 , let m = 5n , if S_m / S_n does not n , then a_2 is

If a_1,a_2,.....a_n are in H.P., then the expression a_1a_2 + a_2a_3 + ... + a_(n-1)a_n is equal to

Let a ,b be positive real numbers. If a, A_1, A_2, b be are in arithmetic progression a ,G_1, G_2, b are in geometric progression, and a ,H_1, H_2, b are in harmonic progression, show that (G_1G_2)/(H_1H_2)=(A_1+A_2)/(H_1+H_2)

Consider a sequence {a_n }with a_1=2 and a_n=(a_(n-1)^ 2)/(a_(n-2)) for all ngeq3, terms of the sequence being distinct. Given that a_1 and a_5 are positive integers and a_5lt=162 then the possible value(s) of a_5 can be (a) 162 (b) 64 (c) 32 (d) 2

Let a_1, a_2 , a_3,...., a_m be the arithmetic means between -2 and 1027 and let g_1, g_2, g_3.........,g_n be the geometric mean between 1 and 1024. g_1 g_2......g_n = 2^45 and a_1 + a_2 + a_3 +....+a_m = 1025 xx 171 The value of n is :

Let a_1, a_2 , a_3,...., a_m be the arithmetic means between -2 and 1027 and let g_1, g_2, g_3.........,g_n be the geometric mean between 1 and 1024. g_1 g_2......g_n = 2^45 and a_1 + a_2 + a_3 +....+a_m = 1025 xx 171 The value of m is :

Let a_1, a_2, a_3.......... be in A.P. and h_1,h_2,h_3..... ,in H.P. If a_1=2 = h_1, and a_30=25=h_30 then a_7h_24+ a_14 + a_17=

Let a_1,a_2,a_3…… ,a_n be in G.P such that 3a_1+7a_2 +3a_3-4a_5=0 Then find common ratio of G.P.

Let (1+x^2)^2(1+x)^n=sum_(k=0)^(n+4)a_k x^k . If a_1 , a_2 and a_3 are in arithmetic progression, then the possible value/values of n is/are a. 5 b. 4 c. 3 d. 2

Let a_1 , a_2 , a_3,.... be terms of an A.P. if (a_1 + a_2 +....+ a_p)/(a_1 + a_2 +...+ a_q) = p^2/q^2. p ne q then a_6/a_21 equals