The sum of terms of a G.P if `a_(1)=3,a_(n)=96` and `S_(n)=189` is

Determine the number of terms in G.P. if a_1=3,a_n=96 and S_n=189 .

Determine the number of terms in a G.P., if a_1=3,a_n=96 ,a n dS_n=189.

Determine the number of terms in G.P. >,ifa_1=3,a_n=96a n dS_n=189.

If the first term of a G.P. a_(1),a_(2),a_(3) is unity such that 4a_(2)+5a_(3) is least, then the common ratio of the G.P. is

Let the sum of the first n terms of a non-constant A.P., a_(1), a_(2), a_(3),... " be " 50n + (n (n -7))/(2)A , where A is a constant. If d is the common difference of this A.P., then the ordered pair (d, a_(50)) is equal to

Some sequences are defined as follows. Find their first four terms : (i) a_(1)=a_(2)=2, a_(n)=a_(n-1)-1, n gt 2 " " (ii) a_(1)=3, a_(n)=3a_(n-1), n gt 1

The terms of a sequence are defined by a_(n)=3a_(n-1)-a_(n-2) for n gt 2 . What is the value of a_(5) if a_(1)=4 and a_(2)=3 ?

Let A be nxxn matrix given by A=[(a_(11),a_(12),a_(13)……a_(1n)),(a_(21),a_(22),a_(23)…a_(2n)),(vdots, vdots, vdots),(a_(n1),a_(n2),a_(n3).a_("nn"))] Such that each horizontal row is arithmetic progression and each vertical column is a geometrical progression. It is known that each column in geometric progression have the same common ratio. Given that a_(24)=1,a_(42)=1/8 and a_(43)=3/16 Let S_(n)=sum_(j=1)^(n)a_(4j),lim_(n to oo)(S_(n))/(n^(2)) is equal to

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)

Let a_n be the n^(th) term, of a G.P of postive terms. If Sigma_(n=1)^(100)a_(2n+1)= 200 and Sigma_(n=1)^(100)a_(2n)=100, " then" Sigma_(n=1)^(200)a_(n)