Arithmetic sequence — Grade 7 Accelerated, what it means and where it is taught
A list that grows by adding the same amount each time.
Taught in Grade 7 Accelerated.
Where it is taught
What uses it later
This idea is needed for:
- Common difference — The constant added each time, in an arithmetic sequence.
Practise this idea
5 questions in the course bank use Arithmetic sequence, in Writing & Transforming Linear Functions, Sequences, Explicit & Recursive.
Problem 1
An arithmetic sequence has a4 = 19 and a9 = 44. Find a1.
Worked answer
4
44 - 19 = 25 over 5 steps, so d = 5
a1 = 19 - 3(5)
= 4
Problem 2
An arithmetic sequence has a1 = -3 and d = 7. Find a20.
Worked answer
130
-3 + 19(7)
= -3 + 133 = 130
Problem 3
An arithmetic sequence has a3 = 11 and a7 = 31. Find d.
Worked answer
5
31 - 11 = 20
20 ÷ 4 = 5
Problem 4
An arithmetic sequence has a1 = 100 and d = -6. Which term is the first negative one?
Worked answer
a_18
100 - 6n + 6 < 0
106 < 6n, so n > 17.67
The 18th term: 100 - 6(17) = -2
Problem 5
Write an explicit formula for the arithmetic sequence with a5 = 23 and a9 = 43.
Worked answer
a_n = 3 + 5(n - 1)
d = 43 - 234 = 5
a1 = 23 - 4(5) = 3
an = 3 + 5(n-1), or 5n - 2