Worksheet: Recursive Sequences

In this worksheet, we will practice working with sequences in recursive form.

Q1:

Find the first five terms of the sequence with general term , where and .

• A
• B
• C
• D

Q2:

The term in a sequence is given by . Find the first six terms of this sequence, given that and .

• A
• B
• C
• D

Q3:

Find the arithmetic sequence in which and .

• A
• B
• C
• D

Q4:

Given that and that for , find a formula for in terms of .

• A
• B
• C
• D
• E

Q5:

Find given and .

• A
• B
• C
• D

Q6:

The term in a sequence is given by . Find the first six terms of this sequence, given that .

• A
• B
• C
• D

Q7:

Find, in terms of the general term of the sequence which satisfies the relation , where and .

• A
• B
• C
• D

Q8:

The sequence , where , is given by

List the next 6 terms .

• A , , , , ,
• B , , , , ,
• C , , , , ,
• D , , , , ,
• E , , , , ,

By listing the elements , give a formula for , in terms of , for .

• A
• B
• C
• D
• E

Give a formula for , in terms of , for .

• A
• B
• C
• D
• E

Give a formula for , in terms of , for .

• A
• B
• C
• D
• E

Give a formula for , in terms of , for .

• A
• B
• C
• D
• E

What is ?

• A
• B
• C
• D
• E

Solve for .

• A
• B
• C
• D
• E

What is the range of the function ?

• Athe set of negative integers
• Bthe set of negative rationals
• Cthe set of postive rationals
• Dthe set of all integers
• Ethe set of positive integers

Q9:

Consider the following sequence of dots.

What is the function such that is the number of dots in the th pattern?

• A
• B
• C
• D
• E

Q10:

The graph represents the triangle wave function , which is periodic, piecewise linear, and defined for all real numbers.

List the values of , , and .

• A1, 1, 1
• B0, 1, 1
• C0, , 1
• D0, 0, 0
• E1, , 0

List the values of , , , and .

• A1, , 1, 1
• B , , 1, 1
• C1, 1, 1, 1
• D1, , 1,
• E1, 1, , 1

What is ?

• A
• B1
• C0
• Dundefined

If we are given that is negative, what can we conclude about the number ?

• A There is some integer for which .
• B is an even integer.
• C There is some integer for which .
• D is an odd integer.

Find the equation of the line segment on which the point lies.

• A
• B
• C
• D
• E

Hence find the value of correct to 3 decimal places.

• A16.850
• B
• C12.283
• D
• E4.429

Q11:

Given the sequence defined by , where and , find the value of .

Q12:

Find the first five terms of the sequence with general term , where and .

• A
• B
• C
• D

Q13:

Find the first five terms of the sequence with general term , where and .

• A
• B
• C
• D

Q14:

Find the first five terms of the sequence with general term , where and .

• A
• B
• C
• D

Q15:

Find the first five terms of the sequence with general term , where and .

• A
• B
• C
• D

Q16:

The term in a sequence is given by . Find the first six terms of this sequence, given that and .

• A
• B
• C
• D

Q17:

The term in a sequence is given by . Find the first six terms of this sequence, given that and .

• A
• B
• C
• D