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For each of the following shape sequences:

i) draw a sequence table for the first six patterns, taking care to use the correct letter for the pattern number and the correct letter for the number of shapes

ii) find a formula for the number of shapes used in terms of the pattern number

iii) use your formula to find the number of shapes used in the 300th pattern.

Number of matches
n=1 n=2 n=3
m-4 m=7 m-10

User Luiz Alves
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2 Answers

3 votes

Answer:

every other 3

Explanation:

User Vlad Khomich
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0 votes

Answer:

Explanation:

It seems like the problem is asking about a sequence of shapes rather than a sequence of matches, so I will assume that the correct information for the problem is:

Number of shapes:

n=1 n=2 n=3

m-4 m=7 m+2

i) Sequence table for the first six patterns:

Pattern number Number of shapes

1 m-4

2 m

3 m+2

4 m+6

5 m+10

6 m+14

ii) Formula for the number of shapes in terms of the pattern number:

From the table, we can see that the number of shapes used in each pattern is increasing by a constant amount of 4. Therefore, we can write the formula as:

Number of shapes = (pattern number - 1) * 4 + m

where m is the number of shapes in the first pattern.

iii) Number of shapes used in the 300th pattern:

To find the number of shapes used in the 300th pattern, we can use the formula and substitute pattern number = 300:

Number of shapes = (300 - 1) * 4 + m

Since we don't know the value of m, we can't determine the exact number of shapes. However, we do know that the number of shapes in the first pattern is either m-4, m, or m+2, depending on the value of m. If we assume the smallest possible value of m, which is 1 (since the number of shapes can't be negative), then the number of shapes in the 300th pattern would be:

Number of shapes = (300 - 1) * 4 + 1-4 = 1195

Therefore, if m = 1, then the number of shapes used in the 300th pattern is 1195. However, if m is greater than 1, then the number of shapes in the 300th pattern would be higher.

User Carol McKay
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