Question

Find $T_n$ in $\frac{1}{2},\frac{1}{4},\frac{1}{6},..........$

Answer 1

It is given that $T_1=\frac{1}{2}$, $T_2=\frac{1}{4}$ and $T_3=\frac{1}{6}$, therefore, the reciprocals are the terms in A.P that are:

$T_1=2$, $T_2=4$ and $T_3=6$

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 $a=2$ and the common difference $d=4-2=2$, therefore,

$T_n=a+(n-1)d=2+(n-1)2=2+2n-2=2n$

Thus, the $n$th term of H.P is $T_n=\frac{1}{2n}$.