Question

If $7$th term of an H.P is $8$ and the $8$th term is $7.$
Find the $28$th term.

Answer 1

$7^{th}$ term of HP= $\frac{1}{7}th$ term of AP= 8

$7^{th}$ term of AP= $\frac{1}{8}$

Similarly $8^{th}$ term of AP= $\frac{1}{7}$

Now d= $\frac{1}{56}$

$8^{th}$ term of AP= $\frac{1}{7}=a+7d$

$\Rightarrow a=\frac{1}{56}$

Now ${28}^{th}$ term of AP is

$a+27d$

$=\frac{1}{56}+27\times \frac{1}{56}$

$=\frac{28}{56}=\frac{1}{2}$

${28}^{th}$ term of HP= 2