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\(\begin{array}  &  &  &  &  1&  &  \\  &  & 2 & 3 & 4 &  &  \\  & 5 & 6 & 7 & 8 & 9 &  \\ 10 & 11 & 12 & 13 & 14 & 15 & 16 \\ &&& \vdots &&& \end{array}\)

Given that the pattern continues, find the second term in the 13th row. 

 Jul 8, 2020
 #1
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Given that the pattern continues, find the second term in the 13th row. 
\(\begin{array}{rrrrrrrrrr}& & & & & \mathbf{1} & & & \\ & & & & 2 & 3 & \mathbf{4} & & \\ & & & 5 & 6 & 7 & 8 & \mathbf{9} & \\ & & 10 & 11 & 12 & 13 & 14 & 15 & \mathbf{16} \\ & 17 & 18 & 19 & 20 & 21 & 22 & 23 & 24 & \mathbf{25} \\ 26 & 27 & 28 & 29 & 30 & 31 & 32 & 33 & 34 & 35 & \mathbf{36} \\ && &&& \vdots && &&& \end{array} \)

 

\(\begin{array}{|r|r|r|r|} \hline & \text{Last term in the row} & \\ \text{row} & = \text{row}^2 &\text{First term in the next row}& \text{Second term in the next row} \\ \hline 1 & 1 & 2 & 3 \\ 2 & 4 & 5 & 6 \\ 3 & 9 & 10 & 11 \\ 4 & 16 & 17 & 18 \\ 5 & 25 & 26 & 27\\ 6 & 36 & 37 & 38 \\ \vdots &\vdots&\vdots&\vdots \\ 12 & 144 & 145 & \color{red}146 \\ \hline \end{array} \)

 

The second term in the 13th row is \(\mathbf{146}\)

 

laugh

 Jul 8, 2020
edited by heureka  Jul 8, 2020

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