`a_1,a_2,a_3,a_4 . . . a_10` are in A.P with d=-3
`b_1,b_2,b_3,b_4 . . . b_10` are in G.P , with r=2
`C_k=a__k+b_k "where" k in (1,10)`
`C_2=12 , C_3=13` then `sum_(k=1)^10 C_k`

Let a_1, a_2, ... , a_(10) be an AP with common difference - 3 and b_1, b_2 , ... , b_(10) be a GP with 10 common ratio 2. Let c_k= a_k + b_k, k = 1, 2, ... , 10 . If c_2 = 12 and c_3= 13 , then sum_(k=1)^(10) ck is equal to _____

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 :

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, ..., a_10, be in G.P. with a_i gt0 for i = 1, 2, ......., 10 and S be the set of pairs (r,k), r, k in NN (the set of natural numbers) for which |(log_e a_1^ra_2^k,log_e a_2^ra_3^k,log_e a_3^ra_4^k), (log_e a_4^ra_5^k,log_e a_5^ra_6^k,log_e a_6^ra_7^k), (log_e a_7^ra_8^k,log_e a_8^ra_9^k,log_e a_9^ra_10^k)|=0. Then the number of elements in S, is

If a_1,a_2,a_3,. . . ,a_n. . . are in A.P. such that a_4−a_7+a_10=m , then sum of the first 13 terms of the A.P.is

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

Suppose four distinct positive numbers a_1,a_2,a_3,a_4 are in G.P. Let b_1=a_1,b_2=b_1+a_2,b_3=b_2+a_3 and b_4=b_3+a_4 . Statement -1 : The numbers b_1,b_2,b_4 are neither in A.P. nor in G.P. and Statement -2 : The numbers b_1,b_2,b_3,b_4 are in H.P.

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).