Modified pyramids

Algebra Level 2

\[\large \begin{array} {c c c c c c c } & 1 & & & & & & 3 \\ & 1+ 3 & & & & & & 5 + 7 \\ & 1 + 3 + 5 & & & & & & 7 + 9 + 11 \\ & 1 + 3 + 5 + 7 & & & & & & 9 + 11 + 13 + 15 \\ & 1 + 3 + 5 + 7 + 9 & & & & & & 11 + 13 + 15 + 17 + 19 \\ & \dots & & & & & & \ldots \\ & \dots & & & & & & \ldots \\ & \dots & & & & & & \ldots \\ \end{array} \]

Let \(a_n\) denote the sum of the first \(n\) positive odd numbers and \(b_n\) as the sum of the next \(n\) positive odd numbers. Above shows the first 5 rows of \(a_n\) and \(b_n\) respectively. What is the value of

\[ \large b_{100} \div a_{100} ?\]

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