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Consider circles, points on its circumference and chords as shown in the figure. Mark two points on the circle and draw a chord. Mark one more point and draw three chords. Continue this process by adding one more point each time.a. Write the number of chords in each figure as a sequence.b. Write the algebraic expression of this sequence.c. Find the number of chords in the 10th figure. |
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Answer» a. No. of chords in figure 1 = 1 No. of chords in figure 2 = 1 + 2 = 3 No. of chords in figure 3 = 1+ 2 + 3 = 6 Sequence of number of chords = 1, 3, 6, 10, … b. No. of chords in figure n = 1 + 2 + 3 + .... + n = \(\frac{n(n+1)}{2}\) c. No. of chords in the 10th figure = \(\frac{10\times11}{2}\) = 55 |
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