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A pattern is formed using sticks of equal length as shown below:a. Write the sequence of number of sticks used in each figure.b. Write the sequence of number of squares and rectangles in each figure,c. Write the algebraic expression in the above two sequences.d. Find the number of sticks and squares in the 10 figure. |
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Answer» a. No of sticks in figure 1 = 1 + 3 = 4 No of sticks in figure 2 = 1 + 3 + 3 = 1+2 × 3 =7 No of sticks in the figure 3 = 1 + 3 × 3 = 10 No of sticks in the figure 4 = 1 + 4 × 3 = 13 Sequence of number of sticks = 4, 7, 10, 13, … (i) b. No of squares and rectangles in the figure 1 = 1 No of squares and rectangles in the figure 2 = 2 + 1 = 3 No of squares and rectangles in the figure 3 =3 + 2+ 1 = 6 No ofsquares and rectangles in the figure 4 = 4 + 3 + 2 + 1 = 10 Sequence of squares and rectangles = 1, 3, 6, 10, …. c. No of sticks in the nth figure 1 = 1+ n × 3 = 3n + 1 No of squares and rectangles in the nth figure = 1 + 2 + 3..... +n = \(\frac{n(n+1)}{2}\) d. No of sticks in the 10th figure = 3 × 10 + 1 = 31 No of squares and rectangles in the 10th figure = \(\frac{10\times11}{2}\) = 55 = 55 |
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