JEE Mains · Maths · STD 11 - 8. sequence and series
If \(x_1 , x_2 , ..... , x_n\) and \(\frac{1}{{{h_1}}},\frac{1}{{{h^2}}},......\frac{1}{{{h_n}}}\) are two \(A.P' s\) such that \(x_3 = h_2 = 8\) and \(x_8 = h_7 = 20\), then \(x_5. h_{10}\) equals
- A \(2560\)
- B \(2650\)
- C \(3200\)
- D \(1600\)
Answer & Solution
Correct Answer
(A) \(2560\)
Step-by-step Solution
Detailed explanation
Suppose \({d_1}\) is the common difference of the \(A.P.\) \({x_1},{x_2},....{x_n}\) then \(\because \) \({x_8} - {x_3} = 5{d_1} = 12 \Rightarrow {d_1} = \frac{{12}}{5} = 2.4\) \( \Rightarrow {x_5} = {x_3} + 2{d_1} = 8 + 2 \times \frac{{12}}{5} = 12.8\) Suppose \({d_2}\) is the…
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