COMEDK · Maths · 5. Sequences and Series
Every term of a geometric progression is positive, and every term is the sum of the two preceding terms. Then the common ratio of the geometric progression is:
- A \(\dfrac{1 + \sqrt{5}}{2}\)
- B \(1\)
- C \(\dfrac{\sqrt{5} - 1}{2}\)
- D \(\dfrac{1 - \sqrt{5}}{2}\)
Answer & Solution
Correct Answer
(A) \(\dfrac{1 + \sqrt{5}}{2}\)
Step-by-step Solution
Detailed explanation
Let the geometric progression be \(a, ar, ar^2, \dots\) Given that every term is positive, we have \(a > 0\) and \(r > 0\). According to the given condition, every term is the sum of the two preceding terms. \(T_n = T_{n-1} + T_{n-2}\) For \(n = 3\), we get: \(ar^2 = ar + a\)…
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