Question 4 of 14intermediate🔧 ApplyNumerical2 marks

Find the sum to infinity in each of the following Geometric Progression. −34,316,−364,…\frac{-3}{4}, \frac{3}{16}, \frac{-3}{64}, \ldots

Correct Answer

-35\frac{3}{5}

Exercise: Exercise 8.3 | Q: 4 | (Page Page 2)
For More Understanding

Explanation

This question tests the application of the sum to infinity formula for a Geometric Progression. The key steps involve identifying the first term and common ratio, verifying that |r| < 1 (which ensures convergence), and then applying the formula S = a/(1-r). The context provides the formula and similar examples showing how to handle negative common ratios.

Solution Steps

  1. Step 1: Identify the first term (a) and common ratio (r).

  2. First term: a = -3/4

  3. Second term: 3/16

  4. Common ratio: r = (3/16) ÷ (-3/4) = (3/16) × (4/-3) = -1/4

  6. Step 2: Verify that |r| < 1.

  7. |r| = |-1/4| = 1/4 < 1, so sum to infinity exists.

  9. Step 3: Apply the formula for sum to infinity.

  10. S = a/(1-r)

  11. S = (-3/4) / (1 - (-1/4))

  12. S = (-3/4) / (1 + 1/4)

  13. S = (-3/4) / (5/4)

  14. S = (-3/4) × (4/5)

  15. S = -3/5

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