3.1 - Sequences

Question 1

I can generate terms of a sequence if I know an adding pattern from one term to another
For example, I can list the terms of a sequence where each number is 10 bigger than the previous:

Answer 1

10, 20, 30, 40, 50, …

Question 2

I can generate terms of a sequence if I know a multiplying pattern from one term to another
For example, I can list the terms of a sequence where each number is 2 times bigger than the previous:

Answer 2

1, 2, 4, 8, 16, …

Question 3

I can generate terms of a sequence if I know an adding expression for the nth term in the sequence.
For example, if the nth term of a sequence is n + 2, then the first five terms are…

Answer 3

2, 3, 4, 5, 6, …, n + 2

The sequence goes up in ones, offset by 2

Question 4

I can generate terms of a sequence if I know an multiplying expression for the nth term in the sequence.
For example, if the nth term of a sequence is 2n + 2, then the first five terms are…

Answer 4

4, 6, 8, 10, 12, …, 2n + 2

The sequence goes up in twos, offset by 2

Question 5

I can find subsequent terms of an integer sequence

For example, 5, 9, 13, 17, …

Answer 5

21

Question 6

I can find subsequent terms of an integer sequence

For example, 1, 2, 4, 8, …

Answer 6

16

Question 7

I can work out a rule for generating the next number in a sequence.
For example, 5, 9, 13, 17, …

Answer 7

add 4

Question 8

I can work out a rule for generating the next number in a sequence.
For example, 1, 2, 4, 8, …

Answer 8

multiply by 2

Question 9

I can work out an expression for the nth term of an arithmetic sequence
For example, 5, 9, 13, 17, …

Answer 9

nth term is 4n + 1

Question 10

I can work out the common difference (d) and first term (a) for an arithmetic sequence
For example, 2nd term is 7, 5th term is 19, what is the common difference (d) and first term (a)?

Answer 10

x, 7, x, x, 19
common difference must be 4
first term must be 3

Question 11

Given the common difference (d) and first term (a), I can know the nth term of an arithmetic sequence
For example, if the common difference is 4, and the first term of a sequence is 3, what is the nth term?

Answer 11

3 + 4(n-1)

= 4n - 1

Question 12

Given the nth term of an arithmetic sequence, I know what the common difference and first term are
For example, if the nth term of a sequence is 4n + 1, what are the common difference and first term?

Answer 12

4n + 1
= 1 + 4n
= 1 + 4(n - 1 + 1)
= 1 + 4(n - 1) + 4
= 5 + 4(n - 1)
First term is 5, common difference is 4

Question 13

Given an arithmetic sequence, I can sum the first n terms of it.
For example, given 4 + 7 + 10 + 13 + … find the sum of the first 5 terms.

Answer 13

• First term is 4
• Common difference is 3
  50th term is 4 + 3 * (5 - 1) = 16
  sum of first 50 terms is 5/2 * (4 + 16) = 50