COMEDK · Maths · 5. Sequences and Series
The sum of four numbers in a geometric progression is 60 , and the arithmetic mean of the first and the last number is 18 . Then the numbers are
- A \(32,16,4,8\)
- B \(32,16,8,2\)
- C \(4,8,16,32\)
- D \(10,8,16,26\)
Answer & Solution
Correct Answer
(C) \(4,8,16,32\)
Step-by-step Solution
Detailed explanation
Let the four numbers in geometric progression be \(a, ar, ar^2, ar^3\). The sum of the four numbers is \(a + ar + ar^2 + ar^3 = 60\). This can be written as \(a(1 + r + r^2 + r^3) = 60\), or \(a(1 + r)(1 + r^2) = 60\). The arithmetic mean of the first and last number is…
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