Geometric Progressions in mathematics are the successions which have a particular relation between the numbers in the series like other progressions. Every number is achieved by multiplying the previous number by a constant value. A definite proportion is maintained between the successive terms of the sequence. Suppose we have a geometric sequence given as follows: s, s * p, s * p2, s * p3, s * p4 and so on. Where, s denotes the first term of the GP and p represents the definite ratio maintained between the terms.
For example, the sequence 8, 16, 32, 64 is a geometric progression with the first term as 8 and the fixed ratio as 16 /8 = 2.
We solve the geometric progression questions as follows: 1st we have to write down the specified facts or figures given regarding the progression. It can be any combination of data that is available to us, it can either be the 1st term and the relation between the numbers or the 1st term and the succeeding term of the progression.
For instance, if the 1st term is 4 and the successive term is 20. The GP can be written as:
4, 4 * 5, 4 * 52, 4 * 53, 4 * 54 and so on.
Next we discuss another concept of maths that is related to the product differentiation of a function. The derivative of a function that contains the product can be solved as follows:
Suppose we have a function: y = f (x) * g (x),
D (y) / D (x) = g (x) D (f (x)) / D (x) + f (x) D (g (x)) / D (x).
We solve such problems by differentiating the two functions simultaneously. These concepts are important in maths and we can free download cbse books to refer these topics. In the next session we will discuss about Rational Exponents.
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