What is the Nth term of a sequence?
The Nth term of a sequence, often written An or Un, is a formula used to generate terms of the sequence
Find the first 5 terms of: An = 100n - n^2
99, 96, 91, 84, 75
A sequence has Nth term: An = n^2 - 19n + 40. For what what value ‘m’ is Am = 60
60 = n^2 -19n + 40
0 = n^2 - 19n - 20
0 = (n+1)(n-20)
n = -1, n = 20 -> m>0, therefore, m = 20
Name some kinds of sequences
- Arithmetic (linear) sequences
- Quadratic sequences
- Geometric sequences
- Fibonacci sequences
What is an arithmetic sequence?
Sequence that changes by the same amount each time (could be adding or subtracting)
What is a quadratic sequence?
Quadratic sequences are sequences that have an^2. They can be identified by looking at 2nd differences.
What is a geometric sequence?
A geometric sequence is a sequence where you multiply the numbers by the same value each time to get a new number (e.g. 5 (x2), 10 (x2), 20 (x2), 40
What is ‘a’ in the Nth term for sequences?
‘a’ is the letter used to represent the first term
What is ‘d’ in the Nth term for sequences?
‘d’ is the (2nd) common difference between values in a sequence
What is the Nth term for ALL arithmetic sequences?
Un = a + (n - 1)d
Find the Nth term for the following sequence: 5, 13, 21, 29
a = 5, d = 8
Un = a + (n - 1)d
Un = 5 + (n - 1)8
Un = 5 + 8n - 8
Un = 8n - 3
What does ‘Sn’ stand for?
Sn = sum of first ‘n’ terms
What is the equation for the sum of the first ‘n’ terms?
Sn = (n/2)(2a + (n - 1)d)
What is the technical term for the second difference in a quadratic sequence?
Constant second difference
What is the layout for the Nth term of a quadratic sequence?
Un = an^2 + bn + c
Practice finding the Nth term for Quadratic + Arithmetic Sequences on GC/notability/DrFrost!!! :(
Good luck!!! You have got this!!! 🥳🥳
