Question

Number of terms in the sequence $1,3,6,10,15,\dots ,5050$ is

• A. 50
• B. 75
• C. 100
• D. 125

Answer 1

Answer: (C)

Let $S=1+3+6+10+15+,\dots ,+t_n(1)$
then $S=1+3+6+10+,\dots ,+t_{n-1}+t_n(2)$
$(1)-(2)\Rightarrow 0=(1+2+3+4+\dots$ to $n$ terms $)-t_n$
$\Rightarrow t_n=\frac{n(n+1)}{2}$
Given, $5050=\frac{n(n+1)}{2}$
$\Rightarrow n^2+n-10100=0$
$\Rightarrow n=\frac{-1\pm \sqrt{1+40400}}{2}$
$=\frac{-1\pm \sqrt{40401}}{2}$
$=\frac{-1\pm 201}{2}=-101,100$
$\therefore n=100.$
$(\because n$ is a positive integer $)$