The largest positive term of the H.P whose 1 st two terms are 5 2 and 23 12 is ____

Question

The largest positive term of the H.P whose 1 st two terms are 5 2 ​ and 23 12 ​ is ____

TestHub · Accepted Answer

First two terms of the corresponding A.P are $\frac{5}{2}$ and $\frac{23}{12}$ Let d be the common difference of the corresponding A.P , Then

$d = \frac{23}{12} - \frac{5}{2} = \frac{- 7}{12}$

Let $a_{n}$ be the nth term of the given H.P. Then ,

$a_{n} = \frac{1}{\frac{5}{2} + ( n - 1 ) ( \frac{- 7}{12} )} = \frac{12}{30 - 7 n + 7} = \frac{12}{37 - 7 n}$

Cleary, $a_{n}$ will be greatest, if $37 - 7 n$ is least $37 - 7 n$ is least for $n = 5$ Hence, $a_{5} = \frac{12}{37 - 35} = 6$ is the largest positive term

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