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 _____

Evaluate :sum_(k=1)^(10)(3+2^(k))

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

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

If A=[(1,-3), (2,k)] and A^(2) - 4A + 10I = A , then k is equal to

Find the value off sum_(k1)^10(2+3^k)

Let S_k be sum of an indinite G.P whose first term is 'K' and commmon ratio is (1)/(k+1) . Then Sigma_(k=1)^(10) S_k is equal to _________.

If sum_(r=1)^(10)r(r-1)10C_(r)=k.2^(9), then k is equal to- -1