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Q.
The fifth term of the H.P., $2,2 \frac{1}{2}, 3 \frac{1}{3}, ...................$ will be
Sequences and Series
Solution:
Series $2,2 \frac{1}{2}, 3 \frac{1}{3}, ........$ are in H.P.
$\Rightarrow \frac{1}{2}, \frac{2}{5}, \frac{3}{10}, ..........$ will be in A.P.
Now, first term $a =\frac{1}{2}$
and common difference $d =-\frac{1}{10}$
So, $5^{th }$ term of the A.P. $=\frac{1}{2}+(5-1)\left(-\frac{1}{10}\right)=\frac{1}{10}$.
Hence, $5^ {th }$ term in H.P. is 10 .