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# Algebra

Sequence and Series - 2

**Geometric Progression:**

Geometric Progression or G.P. is a special sequence in which the successive terms are in a common ratio. For example consider the series 2,4,8,16,32,…..

Here 4/2 = 8/4 = 16/8 = 2. i.e. the terms are in a constant ratio of r.

In general, if the first term is a and the common ratio is r, then the sequence

Sum of n terms:

Let S denotes the sum of n terms of a sequence of which the first term is a and the common ratio is r, then

Example 4: A square is drawn by joining the midpoints of the sides of a given square. A third square is drawn inside the second square in the same way and this process is continued indefinitely. If a side of the first square is 8 cm, the sum of the areas of all the squares such formed (in sq.cm.) is (CAT 1990)

1. 128 2. 120 3. 96 4. None of these