Instructions: Answer all 15 questions. Write your answers in the spaces provided.
For “find the nth term” questions, show your working (differences, second differences, and substitutions) as shown in your notes.
1.
State what is meant by a sequence.
2.
State what the term-to-term rule of a sequence tells you.
3.
State the term-to-term rule for the sequence: 6, 10, 14, 18, …
4.
State the general formula for the nth term of a linear sequence, in terms of $d$ and $c$.
5.
A quadratic sequence has a constant second difference. State how you use this second difference to find the coefficient of $n^2$ in the nth term.
6.
Write the next two terms of the sequence: 4, 9, 14, 19, …
7.
Find the nth term of the linear sequence: 4, 7, 10, 13, …
8.
The nth term of a sequence is $2n + 3$. Find the 15th term.
9.
The nth term of a sequence is $n^3 – 2$. Find the 4th term.
10.
Find the nth term of the quadratic sequence: 3, 6, 11, 18, …
11.
For each sequence below, write the next two terms and state the term-to-term rule.
12.
Consider the linear sequence: 12, 9, 6, 3, …
(a)
Find the nth term of this sequence.
(b)
Use your nth term to find the 10th term.
(c)
Is $-100$ a term in this sequence? Show working to support your answer.
13.
Consider the quadratic sequence: 5, 8, 13, 20, 29, …
(a)
Find the nth term of this sequence.
(b)
Use your nth term to find the 8th term.
14.
Consider the cubic sequence: 0, 7, 26, 63, …
(a)
Find the nth term of this sequence.
(b)
Use your nth term to find the 6th term.
(c)
Is 999 a term in this sequence? Show working to support your answer.
15.
Sequence A has nth term $n^2$. Sequence B is formed by adding 2 to every term of Sequence A.
(a)
Write the first four terms of Sequence A, then the first four terms of Sequence B.
(b)
Write the nth term of Sequence B.
(c)
Explain how the relationship between Sequence A and Sequence B helped you find the nth term of Sequence B.
