1. What are Quadratic Sequences?
Quadratic Sequences:
Quadratic sequences are ordered sets of numbers that follow a rule based on the sequence
n² or the square numbers.
Quadratic sequences always include an n² term.
The resulting sequences don’t have a common difference between each term as linear sequences do, but rather the difference between the differences remains the same.
For example:
Sequence 6, 12, 22, 36
The difference of the sequence is not common. Let's check the second difference,
The second difference is common. Hence the expression will contain a 4n² term
Steps of finding nth term of Quadratic sequence
Step 1: Find the difference between each pair of terms.
Step 2: The difference is changing, so work out the difference between the differences.
Step 3:Divide this value by 2-this gives the coefficient of the n² term (a)
Step 4: Subtract the n² term from each term in the sequence. This will give you a linear sequence.
Step 5: Find the rule for the nth term of the linear sequence and add this on to the n² term.
For example:
Find nth term of the sequence 4 11 20 31 44
2. Examples of Quadratic sequence
Example 1:
The first 5 terms of a quadratic sequence:
4 10 18 28 40
Find an expression, in terms of n, for the nth term of this quadratic sequence.
Also find the next two terms.
Solution:
Example 2:
A quadratic sequence has an nth of 2n²+3n-1 . workout the value of 6th term.
Solution:
Example 3:
A sequence has a nth term of n²-6n+7. Workout which term in the sequence has a value of 23.
Solution:
