Determine the number n in a geometric progression `{a_n}`, if `a_1= 3, a_n= 96` and `S_n= 189`.

Let a_1, a_2 ,........ be positive real numbers in geometric progression. For each n, let A_n, G_n, H_n be respectively the arithmetic mean, geometric mean and harmonic mean of a_1,a_2..........a_n . 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 .

If {a_n} is a G.P. and a_1=4 ,r=5, find a_6 and S_6 .

Find the sum to indicated number of terms of the geometric progressions given below:- 1,-a, a^2,-a^3 , ... n terms (if a ne -1 ).

Write the first five terms of the sequences given below and obtain the corresponding series: a_1=3 , a_n= 3a_(n-1)+2 forall n > 1

Write the first five terms of the sequences given below and obtain the corresponding series: a_1=-1 , a_n= (a_(n-1))/n , n ge2

Find the sum to n terms of the sequence {a_n} , where a_n=5-6n, n in N .

In an AP :- given a = 5, d = 3, a_n = 50 find n and S_n .

Write the first five terms of the sequences given below and obtain the corresponding series: a_1=a_2 =2, a_n=a_(n-1)-1 , n>2

Write the first five terms of the following sequence and obtain the corresponding series : a_1 = 2 , a_n = 2a_(n - 1) + 4 , n ge 2

Determine the number n of terms of the G.P. 3,6,12, .......... so that S_n = 381 .