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Q.
If $18 HM$ 's are interted between $\frac{1}{3}$ and $\frac{1}{41}$ then value of $4^{\text {th }} HM$ is
Sequences and Series
Solution:
let $H _1, H _2, H _3, \ldots ., H _{18}$ are ae $18 HM$ 's between $\frac{1}{3}$ & $\frac{1}{41}$ then
$\frac{1}{ H _1}, \frac{1}{ H _2}, \frac{1}{ H _3} \ldots . . \frac{1}{ H _{18}} \text { are AM's between } 3 \text { and } 41$
$ \Rightarrow \frac{1}{ H _4}=3+4\left(\frac{41-3}{19}\right)=3+8=11 $
$\Rightarrow H _4=1 / 11$