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  • The set of natural numbers N is partitioned into array of rows and columns in the form of matrices as

The set of natural numbers N  is partitioned into array of rows and columns in the form of matrices as M_1=[1]\:\:, M_2=\begin{bmatrix} 2 &3 \\ 4& 5 \end{bmatrix}\:\:, M_3=\begin{bmatrix} 6 &7 &8 \\ 9& 10 & 11\\ 12 &13 & 14 \end{bmatrix}\:\:,...., M_n=[...]\:\:and\:\:so\:\:on

What is  the sum of diagonal element of M_6.

A.  144        B. 441      C. 321       D. 461

Answers (1)

@jeetu

we can clearly observe that the starting element of each matrix as 1,2,6,15,31,56. The diffrence between each diagonal element in a matrix is (n+1) where n is order of matrix. So for M_{6} the sum of diagonal element is \\\frac{n}{2}(a+a_n)=\frac{6}{2}(56+91) = 441

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Safeer PP

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