Let `b_i gt 1 " for " i= 1,2 …., 101` .Suppose loge `b_1` loge `b_2` ….., loge `b_(101)` are in arihtmetic progression (A.P) with the common difference `log_e` 2. Suppose `a_1,a_2,…,a_(101)` are in A.P such that `a_1=b_1 and a_(51). If t= b_1+b_2+….+ b_51 " and " s=a_1+a_2+...+a_(51)` then

Let b_i > 1 for i =1, 2,....,101. Suppose log_e b_1, log_e b_2,....,log_e b_101 are in Arithmetic Progression (A.P.) with the common difference log_e 2 . Suppose a_1, a_2,...,a_101 are in A.P. such that a_1 = b_1 and a_51 = b_51 . If t = b_1 + b_2+.....+b_51 and s = a_1+a_2+....+a_51 then

Let b_(i)gt1" for "i=1,2,"......",101 . Suppose log_(e)b_(1),log_(e)b_(2),log_(e)b_(3),"........"log_(e)b_(101) are in Arithmetic Progression (AP) with the common difference log_(e)2 . Suppose a_(1),a_(2),a_(3),"........"a_(101) are in AP. Such that, a_(1)=b_(1) and a_(51)=b_(51) . If t=b_(1)+b_(2)+"........."+b_(51)" and " s=a_(1)+a_(2)+"........."+a_(51) , then

Let A_1 , A_2 …..,A_3 be n arithmetic means between a and b. Then the common difference of the AP is

Let a_1, a_2, a_3, ...a_(n) be an AP. then: 1 / (a_1 a_n) + 1 / (a_2 a_(n-1)) + 1 /(a_3a_(n-2))+......+ 1 /(a_(n) a_1) =

If a_1,a_2,a_3,...,a_(n+1) are in A.P. , then 1/(a_1a_2)+1/(a_2a_3)....+1/(a_na_(n+1)) is

Let a_1,a_2,a_3…., a_49 be in A.P . Such that Sigma_(k=0)^(12) a_(4k+1)=416 and a_9+a_(43)=66 .If a_1^2+a_2^2 +…+ a_(17) = 140 m then m is equal to

Let a_1,a_2,a_3….., a_(101) are in G.P with a_(101) =25 and Sigma_(i=1)^(201) a_i=625 Then the value of Sigma_(i=1)^(201) 1/a_i eaquals _______.

If the points (a_1, b_1),\ \ (a_2, b_2) and (a_1+a_2,\ b_1+b_2) are collinear, show that a_1b_2=a_2b_1 .

The ratio in which the line segment joining points A(a_1,\ b_1) and B(a_2,\ b_2) is divided by y-axis is (a) -a_1: a_2 (b) a_1: a_2 (c) b_1: b_2 (d) -b_1: b_2

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)