[" Let the terms "a_(1),a_(2),a_(3),...,a_(n)" be in G.P.with common ratio "],[" Let "S_(k)" denote the sum of first "k" terms of this G.P..Prove that "],[S_(m-1)times S_(m)=(r+1)/(r)sum_(1<=i

Let the terms a_(1),a_(2),a_(3),…a_(n) be in G.P. with common ratio r. Let S_(k) denote the sum of first k terms of this G.P.. Prove that S_(m-1)xxS_(m)=(r+1)/r SigmaSigma_(i le itj le n)a_(i)a_(j)

If a_(1), a_(2), a_(3),........, a_(n) ,... are in A.P. such that a_(4) - a_(7) + a_(10) = m , then the sum of first 13 terms of this A.P., is:

If a_(1), a_(2), a_(3),........, a_(n) ,... are in A.P. such that a_(4) - a_(7) + a_(10) = m , then the sum of first 13 terms of this A.P., 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_(3),...a_(n),......... be in A.P.If a_(3)+a_(7)+a_(11)+a_(15)=72, then the sum of itsfirst 17 terms is equal to:

If a_(1),a_(2),a_(3)............ are in A.P. such that a_(4)-a_(7),+a_(10)=m, then sum of 13 terms of this A.P., is;

If a_(1),a_(2),...a_(k) are in A.P. then the equation (S_(m))/(S_(n))=(m^(2))/(n^(2)) (where S_(k) is the sum of the first k terms of the A.P) is satisfied . Prove that (a_(m))/(a_(n))=(2m-1)/(2n-1)

If there be n quantities in G.P., whose common ratio is r and S_(m) denotes the sum of the first m terms, then the sum of their products, taken two by two, is

If there be n quantities in G.P., whose common ratio is r and S_(m) denotes the sum of the first m terms, then the sum of their products, taken two by two, is