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WAEC Further Mathematics 2020 Question 21

Question 21

Sequences and Series

In which of the following series can be the formula S = a/(1 − r) where a is the first term and r is the common ratio, be used to find the sum of all the terms?

  1. A.4 + 8 + 16 + 32 + …
  2. B.½ + 2½ + 12½ + 62½ + …
  3. C.4/81 + 2/27 + 1/9 + 1/6 + …
  4. D.128 + 64 + 32 + 16 + …
Show the answer and explanation

Answer: D (128 + 64 + 32 + 16 + …)

Explanation

The sum to infinity exists only when −1 < r < 1. Only D has such a ratio (r = ½); the others have r = 2, 5 and 3/2.