COMEDK · Maths · 5. Sequences and Series
The product of three numbers in geometric progression is 8 and the sum of the product of the numbers taken in pairs is 14. Find the numbers.
- A \(4, 2, 1\) and \(1, 2, 4\)
- B \(\dfrac{1}{4} , \dfrac{1}{2} , 1\) and \(1, \dfrac{1}{2} , \dfrac{1}{4}\)
- C \(4\sqrt{2} , \sqrt{2} , 1\) and \(1 , \sqrt{2} , 4\sqrt{2}\)
- D \(-4, -2, 1\) and \(1, -2, -4\)
Answer & Solution
Correct Answer
(A) \(4, 2, 1\) and \(1, 2, 4\)
Step-by-step Solution
Detailed explanation
Let the three numbers in geometric progression be \(\dfrac{a}{r}, a, ar\). Given that the product of the numbers is \(8\): \(\dfrac{a}{r} \times a \times ar = 8\) \(a^3 = 8 \Rightarrow a = 2\) Given that the sum of the product of the numbers taken in pairs is \(14\):…
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