A sequence is a set of numbers that follow a specific pattern or rule. Each number in the sequence is called a term.
This sequence increases by 3 each time (+3 pattern)
Same number added each time (common difference)
3, 7, 11, 15, 19... (+4)
20, 17, 14, 11, 8... (-3)
Same number multiplied each time (common ratio)
2, 6, 18, 54, 162... (×3)
80, 40, 20, 10, 5... (×0.5)
The nth term formula lets us find any term in the sequence without listing all previous terms.
nth term = a + (n-1)d
a = first term
d = common difference
n = position of term
First term (a) = 5
Common difference (d) = +4
10th term = 5 + (10-1) × 4 = 5 + 36 = 41
1. What is the next term in the sequence: 3, 7, 11, 15, ?
2. Find the 8th term of the sequence: 2, 5, 8, 11...
Hint: Use nth term = a + (n-1)d
3. What type of sequence is: 1, 3, 9, 27, 81...?