[g_(n)" an "A*P," if "S_(5)+S_(7)=167" and "S_(10)=235" ,sthen find "],[" the "A*P" ."" ,whele sn dend tes the sum of its fiost nitamy "]

In an AP, it is given that S_(5) + S_(7) = 167 "and" S_(10) = 235 , then find the AP, where S_(n) denotes the sum of its first n terms.

If in an A.P, S_n=n^2p and S_m=m^2p , then S_p is equal to

If S_(n) = nP + (n (n - 1))/(2) Q where S_n denotes the sum of the first n terms of an A.P. , then the common difference is

If for a G.P. { t_(n)},t_(2) =-6 and t_(5) =48 find S_(7) .

If in an A.P, S_n=n^2p and S_m=m^2p , then prove that S_p is equal to p^3

For a sequence, if S_n = 7 (4^n - 1) , find the t_n and show that the sequence is a G.P.

If the sum of first n terms of a G.P. is S and the sum of its first 2n terms is 5S, then show that the sum of its first 3n terms is 21S.

If the sum of first n terms of G.P. is S and the sum of its first 2n terms is 5S, then show that the sum of its first 3n terms is 21S.

If in an A.P., S_n=n^2p and S_m=m^2p , where S_r denotes the sum of r terms of the A.P., then S_p is equal to 1/2p^3 (b) m n\ p (c) p^3 (d) (m+n)p^2