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End Of Chapter Exercises

Exercise 3.4See solutions

Find the first five terms of the quadratic sequence defined by:

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?

Constant difference,

Will this always be the case for a linear sequence?

Yes

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.

Given the following pattern of blocks:80b29662534c658fdb3c6af28c0680db.png

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?

Linear

Cubes of volume are stacked on top of each other to form a tower:75098e556f43cc4bc7216d6f7a259c7e.png

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?

Linear

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?

Quadratic

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 schoolsno. of matches
no. of schoolsno. 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 .

See solutions