The set of natural numbers is divided into array of rows and columns in the form of matrices A 1 = [ 1 ] , A 2 = [ 2 3 4 5 ] , A 3 = [ 6 7 8 9 10 11 12 13 14 ] and so on. Let the trace of A 10 be . Find unit digit of ?

Question

The set of natural numbers is divided into array of rows and columns in the form of matrices $A_{1} = [1],$ $A_{2} = [\begin{matrix} 2 & 3 \\ 4 & 5 \end{matrix}],$ $A_{3} = [\begin{matrix} 6 & 7 & 8 \\ 9 & 10 & 11 \\ 12 & 13 & 14 \end{matrix}]$ and so on. Let the trace of $A_{10}$ be $λ$ . Find unit digit of $λ$ ?

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(5)

$First element of matrix A_{10} = 286$ $(10^{th} of sequence 1, 2, 6, 15, \dots)$

$Trace of A_{10} = 286 + 297 + 308 + 319 + \dots + 385 = 3055$

Solution

Ans.
(5)

$First element of matrix A_{10} = 286$ $(10^{th} of sequence 1, 2, 6, 15, \dots)$

$Trace of A_{10} = 286 + 297 + 308 + 319 + \dots + 385 = 3055$

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Solution

Q. The set of natural numbers is divided into array of rows and columns in the form of matrices A1=[1], A2=[2345], A3=[67891011121314] and so on. Let the trace of A10 be λ. Find unit digit of λ

Ans. (5) First element of matrix A10=286 (10th of sequence 1,2,6,15,…) Trace of A10=286+297+308+319+⋯+385=3055

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Ans.
(5)

$First element of matrix A_{10} = 286$ $(10^{th} of sequence 1, 2, 6, 15, \dots)$

$Trace of A_{10} = 286 + 297 + 308 + 319 + \dots + 385 = 3055$