Quadratic Sequences: The Nth Term of a Quadratic Number Sequence
Here, we will be finding the nth term of a quadratic number sequence. A quadratic number sequence has nth term = an² + bn + c
Example 1
Write down the nth term of this quadratic number sequence.
-3, 8, 23, 42, 65...
Step 1: Confirm the sequence is quadratic. This is done by finding the second difference.
Sequence = -3, 8, 23, 42, 65
1st difference = 11,15,19,23
2nd difference = 4,4,4,4
Step 2: If you divide the second difference by 2, you will get the value of a.
4 ÷ 2 = 2
So the first term of the nth term is 2n²
Step 3: Next, substitute the number 1 to 5 into 2n².
n = 1,2,3,4,5
2n² = 2,8,18,32,50
Step 4: Now, take these values (2n²) from the numbers in the original number sequence and work out the nth term of these numbers that form a linear sequence.
n = 1,2,3,4,5
2n² = 2,8,18,32,50
Differences = -5,0,5,10,15
Now the nth term of these differences (-5,0,5,10,15) is 5n -10.
So b = 5 and c = -10.
Step 5: Write down your final answer in the form an² + bn + c.
2n² + 5n -10
Example 2
Write down the nth term of this quadratic number sequence.
9, 28, 57, 96, 145...
Step 1: Confirm if the sequence is quadratic. This is done by finding the second difference.
Sequence = 9, 28, 57, 96, 145...
1st differences = 19,29,39,49
2nd differences = 10,10,10
Step 2: If you divide the second difference by 2, you will get the value of a.
10 ÷ 2 = 5
So the first term of the nth term is 5n²
Step 3: Next, substitute the number 1 to 5 into 5n².
n = 1,2,3,4,5
5n² = 5,20,45,80,125
Step 4: Now, take these values (5n²) from the numbers in the original number sequence and work out the nth term of these numbers that form a linear sequence.
n = 1,2,3,4,5
5n² = 5,20,45,80,125
Differences = 4,8,12,16,20
Now the nth term of these differences (4,8,12,16,20) is 4n. So b = 4 and c = 0.
Step 5: Write down your final answer in the form an² + bn + c.
5n² + 4n
Comments
where does this difference came from, like the 4,8,12,16,20?
- AUTHOR
This would rarely happen, but you can still apply the same method. Just put a decimal before n squared.
What if the second difference is an odd number?
Very good explanation I will recommend this site to any one who has got problem understanding quadratic sequence
its it the same if you get for example 3n+3n+3n+1 like 3 nth terms do u just go and make a third sequence from your second sequence
what do you do if the number only repeats after 4 differences:
1 1 2 7 21
0 1 5 14 1
1 4 9 2
3 5 3
2 4
What is the equation?
Conceptual undertanding is very important for students to comprehend quadratic sequence. Hence, the logic of determining the terms of a given sequence defined by a quadratic formula should be the starting point.
The procedure helps far better but understanding of the concept per se in changing the sequence to arithmetic number sequence should be greatly emphasised.
dat is just dam cul. luving dis site. helpd me a lot.
quad eqns made easy for us math phobs people.
its epic
brilliant i was having trouble with quadratic sequences and this helped a lot thanks
N is number of term.
Dats cul
In step one there's a mistake in the first difference
it should be 11,15,19,23
thanks for this, had trouble understanding for my maths homework
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