Look at the first three stages of a growing pattern of hexagons made using matchsticks. Class 9

Look at the first three stages of a growing pattern of hexagons made using matchsticks. Class 9

Question 1.

Look at the first three stages of a growing pattern of hexagons made using matchsticks. A new hexagon gets added at every stage which shares a side with the last hexagon of the previous stage. Class 9

i. Draw the next two stages of the pattern. How many matchsticks will be required at these stages?

ii. Complete the following table.

iii. Find a rule to determine the number of matchsticks required for the nth stage.

iv. How many matchsticks will be required for the 15th stage of the pattern?

v. Can 200 matchsticks form a stage in this pattern? Justify your answer.

Solution:

Stage 4 will require 21 matchsticks

Stage 5 will require 26 matchsticks

ii.

iii. The rule to determine the number of matchsticks required for the n^th. stage is 5n + 1

iv. Substituting n = 15 in 5n + 1, we get

5(15) + 1 = 76 matchsticks

∴ 76 matchsticks are rquired for 15^th stage.

v. Number of matchsticks = 200

∴ 5n + 1 = 200

∴ 5n = 199

∴ n = $\frac{199}{5}$ = 39.8

Since n = 39.8 is not a whole number 200

∴ 200 matchsticks can't form any stage in this