Sequences with Patterns

Following the pattern, what is the next figure?

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Which of the following has the CORRECT 4th figure?

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Which of the following is the correct formula in finding the nth term of an arithmetic sequence?

• T_n = a + (n - 1)d

• T_n = a + (n + 1)d

• T_n = a - (n - 1)d

• T_n = a +- (n + 1)d

Choose the three steps needed to obtain the n^th term from pictures of patterns.

[This will help in this quiz~]

• Put the pattern number and number of variables in a table

• Remember the number of shapes from the diagram

• Identify the sequence formed

• Use the correct n^th term formula

How many squares would be in the fourth diagram?

(a)  

Pattern number      $1\ \ \ \ 2\ \ \ \ 3\ \ \ \ \ 4$ 
Number of squares   $1\ \ \ \ 5\ \ \ \ 9\ \ \ \ 13$  

Based on the above, how many squares are in the  $n$ th diagram?

(a)  

How many triangles are needed to make the 50^th set of triangles?

[Hint: Find the n^th term first]

(a)  

If there are only 200 sticks, what is the largest set of triangles that could be made?

• 99

• 99.5

• 100

• 100.5

• 101

How many people could be seated at $n$ tables arranged this way? 

(a)  

How many tables would you need if you need to sit 98 people this way?

• 25

• 24