If the first term and common ratio of a G.P. are both `(1/2)(sqrt3+i)`, then the absolute value of its n term

If the first term and common ratio of a G.P are both (1//2) (sqrt(3)+i) , then the absolute value of its n^(th) term is

The first term and common ratio of a G.P. are both positive. The product of first and second term is 9 and that of first and fourth term is 144. Find the third term.

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 its is so, find the its first term, common ratio and the nth term.

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.

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.

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 in G.P. Find its first term and common ratio.

The first term of an A.P. is the same as that of a G.P., the common difference of the one and the common ratio of the other are both 4. If the sum of the first three terms of each series are same, find the fourteenth term of each series.

.Find the G.P., if the common ratio of G.P. is 3, nth term is 486 and sum of first n terms is 728.