Question

1. repeated reasoning how many blocks do you need to add to square 6 to get square 7? to square 9 to get square 10? to square 19 to get square 20? explain.

Explanation:

Step1: Find pattern

Let side - length of square \(n\) be \(n\). Number of blocks in square \(n\) is \(n^2\).

Step2: Calculate difference

For square \(n\) and square \(n + 1\), difference is \((n + 1)^2−n^2=2n + 1\).

Step3: Substitute values

For \(n = 6\), \(2\times6+1 = 13\); for \(n = 9\), \(2\times9+1 = 19\); for \(n = 19\), \(2\times19+1 = 39\).

Answer:

13, 19, 39