Find the sum to infinity in each of the following Geometric Progression.
7.5
Explanation
The question asks for the sum to infinity of a Geometric Progression (G.P.). The provided context establishes the formula for the sum to infinity as S = a / (1-r), valid when the absolute value of the common ratio |r| is less than 1. For the given G.P. 6, 1.2, 0.24..., the first term a is 6. The common ratio r is found by dividing the second term by the first term (1.2/6 = 0.2). Since |0.2| < 1, the formula applies. The calculation yields 7.5, which matches the answer key provided in the context for Exercise 8.3, Question 2.
Solution Steps
First term (a): The first term of the given G.P. is a = 6.
Common ratio (r): The common ratio is calculated by dividing the second term by the first term: r = 1.2 / 6 = 0.2.
Condition Check: Since the numerical value of the common ratio is |r| = 0.2, which is less than 1, the sum to infinity exists.
Formula Application: Using the formula for sum to infinity S = a / (1 - r), we substitute the values.
Calculation: S = 6 / (1 - 0.2) = 6 / 0.8 = 60 / 8 = 7.5.