Question 3 of 14intermediate🔧 ApplyNumerical2 marks

Find the sum to infinity in each of the following Geometric Progression. 5,207,8049,…5, \frac{20}{7}, \frac{80}{49}, \ldots

Correct Answer

353\frac{35}{3}

Exercise: Exercise 8.3 | Q: 3 | (Page Page 2)
For More Understanding

Explanation

This question tests the application of the sum to infinity formula for a Geometric Progression. The student needs to identify the first term and common ratio, verify that |r| < 1, and then apply the formula S = a/(1-r). The context provides the formula and similar examples showing the calculation process.

Solution Steps

  1. Step 1: Identify the first term and common ratio of the G.P. First term a = 5 Common ratio r = (20/7) ÷ 5 = (20/7) × (1/5) = 20/35 = 4/7

  2. Step 2: Verify that |r| < 1 for the sum to infinity to exist. Since |r| = 4/7 < 1, the sum to infinity exists.

  3. Step 3: Apply the formula for sum to infinity. S = a/(1-r) = 5/(1 - 4/7) = 5/(3/7) = 5 × (7/3) = 35/3

  4. Answer: The sum to infinity is 35/3.

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