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 bi gt 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_(1)>1 for i=1,2,......,101. Suppose log_(e)b_(1),log_(e)b_(10) are in Arithmetic progression (A.P.) with the common difference log 2. suppose a_(1),a_(2).........a_(101) are in A.P.such 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,....a11 are in incresing A.P.and if varience of these number is 90 then value of common difference of A.P. is.

If a_1,a_2,a_3,....a_n and b_1,b_2,b_3,....b_n are two arithematic progression with common difference of 2nd is two more than that of first and b_(100)=a_(70),a_(100)=-399,a_(40)=-159 then the value of b_1 is

If the points (a,b),(a_1,b_10 and (a-a_1,b-b_1) are collinear, show that a/a_1=b/b_1

Let a_1,a_2,……a_10 be in A.P. and h_1,h_2,….h_10 be in H.P. If a_1=h_1=2 and a_10 = h_10 =3, then a_4 h_7 is (A) 2 (B) 3 (C) 5 (D) 6

Let a_1,a_2,a_3,... be in A.P. With a_6=2. Then the common difference of the A.P. Which maximises the product a_1a_4a_5 is :

If a_1,a_2,……….,a_(n+1) are in A.P. prove that sum_(k=0)^n ^nC_k.a_(k+1)=2^(n-1)(a_1+a_(n+1))

We know that, if a_1, a_2, ..., a_n are in H.P. then 1/a_1,1/a_2,.....,1/a_n are in A.P. and vice versa. If a_1, a_2, ..., a_n are in A.P. with common difference d, then for any b (>0), the numbers b^(a_1),b^(a_2),b^9a_3),........,b^(a_n) are in G.P. with common ratio b^d. If a_1, a_2, ..., a_n are positive and in G.P. with common ration, then for any base b (b> 0), log_b a_1 , log_b a_2,...., log_b a_n are in A.P. with common difference logor.If x, y, z are respectively the pth, qth and the rth terms of an A.P., as well as of a G.P., then x^(z-x),z^(x-y) is equal to