JEE Mains · Maths · STD 11 - 8. sequence and series
The sum of the first ten terms of an A.P. is \(160\) and the sum of the first two terms of a G.P. is \(8\). If the first term of the A.P. is equal to the common ratio of the G.P. and the first term of the G.P. is equal to common difference of the A.P., then the sum of all possible values of the first term of the G.P. is:
- A \(\dfrac{34}{9}\)
- B \(\dfrac{34}{13}\)
- C \(\dfrac{32}{9}\)
- D \(\dfrac{32}{13}\)
Answer & Solution
Correct Answer
(A) \(\dfrac{34}{9}\)
Step-by-step Solution
Detailed explanation
Let the first term of the A.P. be \(a\) and its common difference be \(d\). Let the first term of the G.P. be \(A\) and its common ratio be \(R\). Given that the sum of the first ten terms of the A.P. is \(160\): \(\dfrac{10}{2} [2a + (10 - 1)d] = 160\) \(5(2a + 9d) = 160\)…
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