0
It's simpler than you might think..
The general equation you need is this:
a+b+c 4a+2b+c 9a+3b+c 16a+4b+c
3a+b 5a+b 7a+b
2a 2a
Basically, the second row down is the difference between the terms of the sequence itself (top row). And the 3rd row down is the differences of the differences (:P).
I'm not good enough with words to explain how to find the nth term so I'll give you an example:
3 7 15 27 43
4 8 12 16
4 4 4
First, you need to know this formula:
2a=diff. of diff. (4 in this example)
3a+b= 1st of the differences (4 in this example)
A+B+C= 1st term (3 in this example)
So let's work it out:
2a=4
(so) a=2
3a+b= 4
(3a would be 3 times 2 so) 6+b=4
(To get from 6 to 4 you need to minus two so) b= -2
(To get to c you need a+b and then work out the difference of that and the 1st term.)
a+b= 0
(2-2= 0)
(The difference of the first term and a+b gives you c)
3-0= 3
c=3
Hope this has helped :S
What else can I help you with?
Do sequences with an equivalent second difference have a quadratic nth term?
yes
What are all the nth term formulas?
Nth term formulas are mathematical expressions used to find the position or value of a term in a sequence. The most common types include arithmetic sequences, where the nth term is given by ( a_n = a_1 + (n-1)d ) (with ( d ) as the common difference), and geometric sequences, represented by ( a_n = a_1 \times r^{(n-1)} ) (with ( r ) as the common ratio). For other types of sequences, such as quadratic or exponential, the nth term can be derived using specific polynomial or exponential functions. Each formula is tailored to the pattern of the sequence in question.
What is the nth term for the sequence 5 15 29 47 69?
To find the nth term of the sequence 5, 15, 29, 47, 69, we first determine the differences between consecutive terms: 10, 14, 18, and 22. The second differences are constant at 4, indicating that the nth term is a quadratic function. By fitting the quadratic formula ( an^2 + bn + c ) to the sequence, we find that the nth term is ( 2n^2 + 3n ). Thus, the nth term of the sequence is ( 2n^2 + 3n ).
What is triangular sequences nth term rule?
0.5n(n+1)
How do I find the nth term in a quadratic sequence?
To find the nth term in a quadratic sequence, first identify the first and second differences of the sequence. The second difference should be constant for a quadratic sequence. Use this constant to determine the leading coefficient of the quadratic equation, which is half of the second difference. Next, use the first term and the first difference to derive the complete quadratic formula in the form ( an^2 + bn + c ) by solving for coefficients ( a ), ( b ), and ( c ) using known terms of the sequence.
Do sequences with an equivalent second difference have a quadratic nth term?
yes
What are all the nth term formulas?
Nth term formulas are mathematical expressions used to find the position or value of a term in a sequence. The most common types include arithmetic sequences, where the nth term is given by ( a_n = a_1 + (n-1)d ) (with ( d ) as the common difference), and geometric sequences, represented by ( a_n = a_1 \times r^{(n-1)} ) (with ( r ) as the common ratio). For other types of sequences, such as quadratic or exponential, the nth term can be derived using specific polynomial or exponential functions. Each formula is tailored to the pattern of the sequence in question.
What is the formula for the nth Term of these sequences 13 21 29 37 45 ...?
nth term = 5 +8n
What is the nth term for the sequence 5 15 29 47 69?
To find the nth term of the sequence 5, 15, 29, 47, 69, we first determine the differences between consecutive terms: 10, 14, 18, and 22. The second differences are constant at 4, indicating that the nth term is a quadratic function. By fitting the quadratic formula ( an^2 + bn + c ) to the sequence, we find that the nth term is ( 2n^2 + 3n ). Thus, the nth term of the sequence is ( 2n^2 + 3n ).
What is the nth term of the quadratic sequence 4 7 12 19 28?
nth term is n squared plus three
What is triangular sequences nth term rule?
0.5n(n+1)
How do I find the nth term in a quadratic sequence?
To find the nth term in a quadratic sequence, first identify the first and second differences of the sequence. The second difference should be constant for a quadratic sequence. Use this constant to determine the leading coefficient of the quadratic equation, which is half of the second difference. Next, use the first term and the first difference to derive the complete quadratic formula in the form ( an^2 + bn + c ) by solving for coefficients ( a ), ( b ), and ( c ) using known terms of the sequence.
What is the nth term for 8 13 20 29 40?
To find the nth term in this sequence, we first need to determine the pattern. The differences between consecutive terms are 5, 7, 9, and 11 respectively. These differences are increasing by 2 each time. This indicates that the sequence is following a quadratic pattern. The nth term for this sequence can be found using the formula for the nth term of a quadratic sequence, which is Tn = an^2 + bn + c.
What is the 9th term in the quadratic sequence 2 5 10 17 26?
To find the nth term in a quadratic sequence, we first need to determine the pattern. In this case, the difference between consecutive terms is increasing by 3, 5, 7, 9, and so on. This indicates a quadratic sequence. To find the 9th term, we need to use the formula for the nth term of a quadratic sequence, which is given by: Tn = an^2 + bn + c. By plugging in n=9 and solving for the 9th term, we can find that the 9th term in this quadratic sequence is 74.
What is the nth term rule of the quadratic sequence below8,16,26,38,52,68,86,..?
94 and you skip it by 8's
What is the nth term rule of the quadratic sequence below4,6,10,16,24,34,46sorry for asking a lot of questions?
nevermind i got it!!
What is the first 5 sequences is the nth term is 30-4n?
Wow you really can't spell.
