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Differentiation of infinite series

The sum of an infinite geometric series is 2 and the sum of the geometric series made from the cubes of this infinite series is 24. Then the series is:

The sum of an infinite geometric series is 6. If its first terms is 2, find its common ratio.

The sum of an infinite geometric series is 15 and the sum of the squares of these terms is 45.Find the series.

The sum of an infinite geomwtric series is 20 and the sum of the squares of these terms is 100. Find the series.

The sum of first two terms of an infinite geometric series is 15 and each term is equal to the sum of all the terms following it, find the series.

If the sum of an infinite G.P is 32 and the some of its first two terms is 24, find the series.

The first term of an infinite G..P is 1 and any term is equal to the sum of all the succeeding terms. Find the series.