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2.6 Calculate which figure number will have 97 squares?

Mathematics

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Answer

25

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Here's the solution for question 2.2.6:

2.2.6 Calculate which figure number will have 97 squares?

  1. Recall the formula for the number of squares in Figure nn from Activity 2.

    The number of squares in Figure nn is given by the formula Sn=1+(n−1)4S_n = 1 + (n-1)4.

  2. Set the formula equal to 97 and solve for nn.

    1+(n−1)4=971 + (n-1)4 = 97 (n−1)4=97−1(n-1)4 = 97 - 1 (n−1)4=96(n-1)4 = 96 n−1=964n-1 = \frac{96}{4} n−1=24n-1 = 24 n=24+1n = 24 + 1 n=25n = 25

    Figure number 25\boxed{25} will have 97 squares.

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