Question

Find $T_{10}$ in $\frac{1}{7},\frac{1}{4},1,........$

Answer 1

It is given that $T_1=\frac{1}{7}$, $T_2=\frac{1}{4}$ and $T_3=1$, therefore, the reciprocals are the terms in A.P that are:

$T_1=7$, $T_2=4$ and $T_3=1$

We know that the formula for the $n$th term of an A.P is $T_n=a+(n-1)d$, where $a$ is the first term, $d$ is the common difference.

Here, the first term $a=7$, the common difference $d=4-7=-3$ and $n=10$, therefore,

$T_{10}=7+(10-1)(-3)=7+(9\times -3)=7-27=-20$

Thus, the $10$th term of H.P is $T_{10}=-\frac{1}{20}$.