Arithmetic sequences

Question 1

linear/arithmetic sequence

Answer 1

a sequence of numbers where the difference between consecutive terms in constant

Question 2

How do you find the formula for the nth term of the sequence?

Answer 2

1) find the constant difference between the consecutive terms in the sequence (a)
2) this becomes [an]
3) work out the sequence of [an]
4) work out what you need to +/- from the new sequence to get back to the original (+/-b)
5) nth term = [an +/- b)

Question 3

Here is a sequence of numbers:
1, 5, 9, 13, 17

Work out a formula for the nth term of the sequence

Answer 3

difference = 4

4n: 4, 8, 12, 16, 20
- 3
sequence: 1, 5, 9, 13, 17

nth term = 4n - 3

Question 4

Here are the first five terms of an arithmetic sequence:
3, 7, 11, 15, 19

a) write down an expression for the nth term
b) is 89 a term in the sequence?

Answer 4

a) 4n - 1

b) 89 = 4n - 1
90 = 4n
n = 22.5
no

Question 5

Here is a sequence:
26, 23, 20, 17

a) Which of these is a formula for the nth term?
3n + 26
-3n + 26
3n + 29
-3n + 29

b) Work out the first negative term of the sequence

Answer 5

a) -3n + 29

b) -1 = -3n + 29
-30 = -3n
3n = 30
n = 10
the 10th term is -1

Question 6

A sequence is:
7, 9, 11, 13

What would be a sequence of 3n?

Answer 6

3, 6, 9, 12…

n is not the actual term

Question 7

If a question wants the ‘first term of the sequence that is negative’, what do you do?

Answer 7

• set the formula as equal to -1
• if it solves into an integer use the value of n to check if there is a term before -1
• if there isn’t, the answer is -1
• if it doesn’t solve into an integer round down and check if that term is negative
• if it is, check the terms before that until you find one that is positive, then that value is the answer

-if it isn’t, round up from the previous answer and use that value