Determine the number of terms in a G.P., if `a_(1)=3,a_(n)=96andS_(n)=189`

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

Using Mathematical Induction, the number a_(n) 's are defined by a_(0)=1,a_(n+1)=3n^(2)+n+a_(n)(nle0)" then "a_(n)=

Let the sum of the first n terms of a non-constant AP 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 AP, then the ordered pair (d, a_(50)) is equal to

Write the first five terms of each of the sequences and obtain the corresponding series: a_(1)=3,a_(n)=3a_(n-1)+2 for all n gt 1

Let a_(1), a_(2) ...be positive real numbers in geometric progression. For n, if A_(n), G_(n), H_(n) are respectively the arithmetic mean, geometric mean and harmonic mean of a_(1), a_(2),..., a_(n) . Then, find an expression for the geometric mean of G_(1), G_(2),...,G_(n) in terms of A_(1), A_(2),...,A_(n), H_(1), H_(2),..., H_(n)

Find the indicated terms of the sequences whose nth terms are given by a_(n)=(5n)/(n+2), a_(6) and a_(13)

Find the indicated terms of the sequences whose nth terms are given by a_(n)=-(n^(2)-4), a_(4) and a_(11)