FIND THE RULE WHICH GIVES THE NUMBER OF MATCHSTICKS

Example 1 :

(a)  Complete a table for the first four figures in the pattern:

(b)  Find how many matches are required to make the:

i)  10^th figure      ii) 50^th figure

(c) Write a description of the pattern in words.

(d) Predict a general rule for finding the number of matches M in the n^th figure

Solution :

(a)

(b)  Number of match sticks in the 1^st picture  =  7

Number of match sticks in the 2^nd picture  =  10

Number of match sticks in the 3^rd picture  =  13

7, 10, 13, .............

To get the next term, we add 3 by the preceding term.

General term  =  3n+4

(i)  10^th term  =  3(10)+4  ==>  34

(ii)  50^th term  =  3(50)+4  ==>  154

(c)  To get the number of match sticks in each figure,  we use number times 3 plus 4.

(d) General rule  =  3n+4

Example 2 :

Consider the pattern:

(a)  Draw the next two figures and hence complete:

b) Find how many matches would be required to make the:

(i) 6^th figure  (ii) 20^th figure.

c)  Copy and complete:

“The number of matches is the figure number ......”.

d) Write a general rule for determining the number of matches M in the nth figure

Solution :

b) (i) 6^th figure (ii) 20^th figure.

General formula  =  3n

If n = 6, then 3n  ==>  3(6)  == > 18

If n = 20, then 3n  ==>  3(20)  == > 60

c)  “The number of matches is the figure number

times 3

d) M  =  3n

Example 3 :

a) Draw the next two section type fences.

b)  If S is the number of steel lengths Wiktor requires to make an n - section fence, copy and complete the following table

c) Determine the formula which connects S and n.

d)  If Victor has an order for a 44-section fence, how many lengths of steel are required to make it?

Solution :

(a)

(b)  

5, 9, 13, .................

every time 4 is added.

c)  S - number of lengths and n - number of section

S  =  4n+1

d)  Number of lengths of steel are required 

S₄₄  =  4(44) + 1

=  176+1

=  177

So, 177 steels are needed.

Example 4 :

Builder Ben is experimenting with toothpicks to investigate housing designs:

(a)   Draw toothpick diagrams for 4 houses and 5 houses.

(b)  If T is the number of toothpicks required to make h houses and complete the table.

(c)  Find the formula which connects T and h.

(d)  If Ben wanted to build 25 houses in a row, how many tooth picks would he need ?

Solution :

(a)  

(b)  

(c)  By writing number of toothpicks required as sequence, we get

6, 11, 16, 21, ................

Every time 5 is added.

So, T  =  5h + 1

T-number of toothpicks and h - houses

(d)  If h  =  25

T  =  5(25) + 1

T  =  125+1

T  =  126

So, the number of toothpicks required to make 25th house is 126.

Example 5 :

Consider the pattern:

a) Copy and complete the table of values:

b) Write a rule linking n and M.

Solution :

(a)  Number of matchsticks used in 1^st picture  =  2

Number of matchsticks used in 2^nd picture  =  4

Number of matchsticks used in 3^rd picture  =  6

using this pattern we can fill up

(b)  Number of matches(M)  =  2n

Example 6 :

Consider the pattern:

a) Copy and complete the table of values :

b) Write a rule linking n and M.

Solution :

(a)  Number of matchsticks used in 1^st picture  =  3

Number of matchsticks used in 2^nd picture  =  7

Number of matchsticks used in 3^rd picture  =  11

By observing this, we notice every time 4 is added.

(b)  Number of matches (M)  =  4n - 1

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