COMEDK · Maths · 5. Sequences and Series
A geometric progression consists of an even number of terms. If the sum of all the terms is 5 times the sum of the terms occupying odd places, then the common ratio of the G.P is
- A 4
- B 2
- C 5
- D 3
Answer & Solution
Correct Answer
(A) 4
Step-by-step Solution
Detailed explanation
Let the geometric progression be \(a, ar, ar^2, ar^3, \dots, ar^{2n-1}\), where the number of terms is \(2n\). The sum of all terms is \(S = a + ar + ar^2 + \dots + ar^{2n-1} = a \dfrac{r^{2n} - 1}{r - 1}\). The terms occupying odd places are \(a, ar^2, ar^4, \dots, ar^{2n-2}\).…
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