Question

The number of terms in the sequence $1,3,6,10,15,21,......,5050$ is.

• A. $50$
• B. $100$
• C. $101$
• D. $105$

Answer 1

The correct option is B $100$

Let number of terms be $n$
and $S_n=1+3+6+10+15+21+\cdots +T_n$........... {i}
$\therefore S_{n-1}=1+3+6+10+15+21+\cdots +T_{n-1}$.............. {ii}
Now, subtracting {ii} from {i} by shifting one term, we get
$T_n=S_n-S_{n-1}=1+2+3+4+5+6+\cdots +n=\frac{n(n+1)}{2}$
Given $T_n=5050=\frac{n(n+1)}{2}\Rightarrow n=100$
Hence, option B is correct.