Question

The $n^{th}$ term of the sequence $\frac{1}{p}$, $\frac{1+2p}{p}$, $\frac{1+4p}{p}$,... is

• A. $\frac{1+2np+2p}{p}$
• B. $\frac{1-2np-2p}{p}$
• C. $\frac{1+2np-2p}{p}$
• D. $\frac{1+2np}{p}$

Answer 1

The correct option is C $\frac{1+2np-2p}{p}$

Sequence, $\frac{1}{p}$, $\frac{1+2p}{p}$, $\frac{1+4p}{p}$........
Here $a=\frac{1}{p}$, $d$ $=$ $\frac{1+2p}{p}$ $-\frac{1}{p}$

$\Rightarrow$ $d=\frac{1+2p-1}{p}$
$\Rightarrow$ $d=2$

$\therefore t_n$ $=$ $\frac{1}{p}+(n-1)2$ $=$ $\frac{1}{p}$ + $\frac{2n-2}{1}$ $\Rightarrow$ $t_n$

$=$ $\frac{1+2np-2p}{p}$