Q117 / 200 · TS EAMCET 2002 · Mathematics
In the sequence, $(1,2,3),(4,5,6),(7,8,9,10)$ $\ldots$ of sets, the sum of elements in the 50th set is
- Correct answerA$62525$
- B$65225$
- C$56255$
- D$557625$
Solution
First term of each sets are $1,2,4,7, \ldots$
Let
$$
\begin{aligned}
& S=1+2+4+7+\ldots+T_n \\
& S=1+2+4+\ldots+T_n
\end{aligned}
$$
On subtracting, we get
$$
\begin{aligned}
& 0=1+1+2+3+\ldots-T_n \\
& T_n=1+(1+2+3+\ldots(n-1) \text { terms }) \\
& T_n=1+\frac{(n-1) n}{2} \\
& T_{50}=1+\frac{49 \times 50}{2} \\
& \therefore \quad T_{50}=1226 \\
&
\end{aligned}
$$
$\Rightarrow$ First term of 50th set is 1226 , therefore series is $1226,1227, \ldots 50$ terms
$$
S=\frac{50}{2}[2 \cdot 1226+49]=62525
$$
Hence, the correct answer is option: 'A'.