Given a G.P. with a= 1,`r= sqrt2`. Find `S_20`.

Given a G.P. with a= 729 and 7th term 64, determine S_7 .

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

Find the value to three places of decimals of the following, it is given that: sqrt2=1.414, sqrt5=2.236 and sqrt10=3.162 (sqrt2+1)/sqrt5

Find the value to three places of decimals of the following, it is given that: sqrt2=1.414, sqrt5=2.236 and sqrt10=3.162 (sqrt10-sqrt5)/sqrt2

Area of the triangle with vertices (a, b), (x_1,y_1) and (x_2, y_2) where a, x_1,x_2 are in G.P. with common ratio r and b, y_1, y_2 , are in G.P with common ratio s, is

We are given two G.P.'s, one with the first term 'a' and common ratio ‘r’ and the other with first term ‘b’ and common ratio ‘s’. Show that the sequence formed by the product of corresponding terms is a G.P. Find its first term and the common ratio. Show also that the sequence formed by the quotient of corresponding terms is G.P. Find its first term and common ratio.

Find S_oo of G.P. whose first term is 28 and the fourth term is 4/49 .

Evaluate: 15/(sqrt10+sqrt20+sqrt40-sqrt5-sqrt80) it is given that sqrt5=2.236 and sqrt10=3.162

The terms of a G.P. with first term ‘a’ and common ratio ‘r’ are squared. Is the resulting sequence also a G.P. ? If it is so, find its first term, common ratio and the nth term.

A body of mass 20g is rotating around a pole 50 cm away with a frequency 5 r.p.s.Find the rotational kinetic energy of the body.