Find the first five terms of the quadratic sequence defined by:
End Of Chapter Exercises
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Determine whether each of the following sequences is:
 a linear sequence,
 a quadratic sequence,
 or neither.
Quadratic sequence
Quadratic sequence
Quadratic sequence
Quadratic sequence
Quadratic sequence
Quadratic sequence
Linear sequence
Linear sequence
Quadratic sequence
Quadratic sequence
Quadratic sequence
Linear sequence
Quadratic sequence
Given the pattern: , determine the value of if the pattern is linear.
Given , for which value of does ?
Given , find .
Given , for which value of does ?
Given , find .
Given , for which value of does ?
For each of the following patterns, determine:
 the next term in the pattern,
 and the general term,
 the tenth term in the pattern.
For each of the following sequences, find the equation for the general term and then use the equation to find .
Given:
Write down the first five terms of the sequence.
What do you notice about the difference between any two consecutive terms?
Will this always be the case for a linear sequence?
Given the following sequence:
Determine the equation for the general term.
Calculate how many terms there are in the sequence.
Given
Thabang determines that the general term is . Is he correct? Explain.
Thabang's general term describes a linear sequence and this is a quadratic sequence.
Cristina determines that the general term is . Is she correct? Explain.
Draw pattern .
Complete the table below:
pattern number  
number of white blocks 
pattern number  
number of white blocks 
Is this a linear or a quadratic sequence?
Complete the table for the height of the tower:
tower number  
height of tower 
tower number  
height of tower 
What type of sequence is this?
Now consider the number of cubes in each tower and complete the table below:
tower number  
number of cubes 
tower number  
number of cubes 
What type of sequence is this?
Determine the general term for this sequence.
How many cubes are needed for tower number ?
How high will a tower of cubes be?
A quadratic sequence has a second term equal to , a third term equal to and a fourth term equal to .
Determine the second difference for this sequence.
Hence, or otherwise, calculate the first term of the pattern.
There are schools competing in the U16 girls hockey championship and every team must play two matches — one home match and one away match.
Use the given information to complete the table:
no. of schools  no. of matches 
no. of schools  no. of matches 
Calculate the second difference.
Determine a general term for the sequence.
How many matches will be played if there are schools competing in the championship?
If matches must be played, how many schools are competing in the championship?
The first term of a quadratic sequence is , the third term is and the common second difference is . Determine the first six terms in the sequence.
Challenge question:
Given that the general term for a quadratic sequences is , let be the first difference and be the second common difference.
Show that .
Show that .
Show that .
Hence, show that .
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