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Question: Answered & Verified by Expert
If $\frac{1}{4}, \mathrm{a}, \mathrm{b}, \frac{1}{19}$ form a H.P. then the values of a and $\mathrm{b}$ are respectively
MathematicsSequences and SeriesMHT CETMHT CET 2020 (15 Oct Shift 1)
Options:
  • A $\frac{1}{12}, \frac{1}{15}$
  • B $\frac{1}{5}, \frac{1}{7}$
  • C $\frac{1}{9}, \frac{1}{14}$
  • D $\frac{1}{11}, \frac{1}{17}$
Solution:
1771 Upvotes Verified Answer
The correct answer is: $\frac{1}{9}, \frac{1}{14}$
$\frac{1}{4}, a, b, \frac{1}{19} \longrightarrow$ H.P.
$4, \frac{1}{a}, \frac{1}{b}, 19 \rightarrow$ AP
$a=\frac{1}{9}, b=\frac{1}{14}$

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