Question

If the${20}^{th}$ an H.P. is $1$ & the ${30}^{th}$ term is $\frac{-1}{17}$ then find its largest term

Answer 1

$\frac{1}{a_n}=\frac{1}{a_1+(n-1)d}$

For $n=20$

$\frac{1}{a_{20}}=\frac{1}{a_1+(20-1)d}$

$\Rightarrow \frac{1}{1}=\frac{1}{a_1+19d}$

$\Rightarrow a_1+19d=1⟶1$

For $n=30$

$\frac{1}{a_{30}}=\frac{1}{a_1+(30-1)d}$

$\Rightarrow \frac{1}{-17}=\frac{1}{a_1+29d}$

$\Rightarrow a_1+29d=-17⟶2$

$\Rightarrow d=-\frac{9}{5}$

$\Rightarrow a_1=\frac{176}{5}$

Largest term will be $\frac{176}{5}$