Consider an A.P. `a_1, a_2, a_n , ` and the G.P. `b_1,b_2, ,b_n , ` such that `a_1=b_1=1,a_9=b_9` and `sum_(r=1)^9a_r=369 ,` then `b_6=27` (b) `b_7=27` `b_8=81` (d) `b_9=81`

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 .

Let A={a_1,a_2,a_3,.....} and B={b_1,b_2,b_3,.....} are arithmetic sequences such that a_1=b_1!=0, a_2=2b_2 and sum_(i=1)^10 a_i=sum_(i=1)^15 b_j , If (a_2-a_1)/(b_2-b_1)=p/q where p and q are coprime then find the value of (p+q).

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

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

In direct proportion a_1/b_1 = a_2/b_2

Let a_1,a_2," ..."a_10 be a G.P. If a_3/a_1=25," then "a_9/a_5 equals

a_1, a_2, a_3 …..a_9 are in GP where a_1 lt 0, a_1 + a_2 = 4, a_3 + a_4 = 16 , if sum_(i=1)^9 a_i = 4 lambda then lambda is equal to

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 .