Observe the toothpick pattern given below:

(a) Imagine that this pattern continues. Complete the table to show the number of toothpicks in the first six terms.

(b)Make a graph by taking the pattern numbers on the horizontal axis and the number of toothpicks on the vertical axis. Make the horizontal axis from 0 to 10 and the vertical axis from 0 to 30.

(c) Use your graph to predict the number of toothpicks in patterns 7 and 8. Check your answers by actually drawing them.

(d) Would it make sense to join the points on this graph? Explain.

Question

Philoid · Accepted Answer

(a) Let us observe the pattern given and complete the table.

Pattern and toothpicks are related as follows

1→ 4,

2→ 4 + 3 = 7

3→ 7 + 3 = 10

4→ 10 + 3 = 13

5→ 13 + 3 = 16

6→ 16 + 3 = 19

∴ fill the above details in the table. we get,

(b) The graph is plotted as the pattern numbers on the horizontal axis and the number of toothpicks on the vertical axis.

(c) The graph follows y = 3x + 1 pattern.

If x = 7 then y = (3 ×7) + 1 = 22

If x = 8 then y = (3 ×8) + 1 = 25

(d) Yes, X and Y follows the y = 3x + 1 pattern.