Question

If the product of $n$ matrices
$\left[\begin{array}{cc}1& 1\\ 0& 1\end{array}\right]\left[\begin{array}{cc}1& 2\\ 0& 1\end{array}\right]\left[\begin{array}{cc}1& 3\\ 0& 1\end{array}\right]\dots \dots \left[\begin{array}{cc}1& n\\ 0& 1\end{array}\right]$ is equal to the matrix $\left[\begin{array}{cc}1& 378\\ 0& 1\end{array}\right]$ then the value of $n$ is equal to

• A. $26$
• B. $27$
• C. $377$
• D. $378$

Answer 1

The correct option is B $27$

$\Rightarrow \sum n=378$

$\Rightarrow \frac{n(n+1)}{2}=378$

$\Rightarrow n(n+1)=756$

$\Rightarrow n=27$ [B]