a_1, a_2, a_3 হলে। . . এবং b_1 , b_2 ,b_3 ... দুটি AP এবং a_1=2 , a_(10)=3 এবং a_1 b_1 =1...

Let a_1,a_2,a_3 ….and b_1 , b_2 , b_3 … be two geometric progressions with a_1= 2 sqrt(3) and b_1= 52/9 sqrt(3) If 3a_99b_99=104 then find the value of a_1 b_1+ a_2 b_2+…+a_nb_n

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 .

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

Three distinct numbers a_1 , a_2, a_3 are in increasing G.P. a_1^2 + a_2^2 + a_3^2 = 364 and a_1 + a_2 + a_3 = 26 then the value of a_10 if a_n is the n^(th) term of the given G.P. is:

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).

Let the sequence a_1 , a_2 , a_3 ......... a_n form an A.P. then a_1^2 - a_2^2 + a_3^2 - a_4^2 +.....+ a_(2n-1)^2 - a_(2n)^2 is equal to:- (1) n/(2n-1)(a_1^2-a_(2n)^2) (2) (2n)/(n-1)(a_(2n)^2-a_1^2) (3) n/(n+1)(a_1^2+a_(2n)^2) (4)none of these

Let the sequence a_1 , a_2 , a_3 ......... a_n form an A.P. then a_1^2 - a_2^2 + a_3^2 - a_4^2 +.....+ a_(2n-1)^2 - a_(2n)^2 is equal to:- (1) n/(2n-1)(a_1^2-a_(2n)^2) (2) (2n)/(n-1)(a_(2n)^2-a_1^2) (3) n/(n+1)(a_1^2+a_(2n)^2) (4)none of these