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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.
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What is the sequence of 10 8 6 4?
10-2x for x = 0, 1, 2, 3, ... Since the domain of an arithmetic sequence is the set of natural numbers, then the formula for the nth term of the given sequence with the first term 10 and the common difference -2 is an = a1 + (n -1)(-2) = 10 - 2n + 2 = 12 - 2n.
What is the nth term for the sequence 10 17 24 31 38?
The nth term in the arithmetic progression 10, 17, 25, 31, 38... will be equal to 7n + 3.
The first five terms of a certain sequence are 2 5 10 17 and 26 What is the next term?
37
What is the nth term of 4 10 28 82?
Oh, what a happy little sequence we have here! To find the pattern, we can see that each term is generated by multiplying the previous term by 2 and then adding 2. So, the nth term can be found using the formula 2^n * 2 - 2. Isn't that just a delightful little formula?
What is the nth term for 3 10 17 24 31?
You can see that all the numbers go up by 7. This means that the first part of the nth term rule for this sequence is 7n. Now, you have to find out how to get from 7 to 3, 14 to 10, 21 to 17 ... this is because we are going up in the 7 times table. To get from the seventh times table to the sequence, you take away four. So the answer is : 7n-4
What is the answer to this quadratic sequence 6 18 40 72 114?
To find the next term in the quadratic sequence 6, 18, 40, 72, 114, we first determine the second differences. The first differences are 12, 22, 32, and 42, while the second differences are 10, 10, and 10, indicating it is indeed quadratic. The next first difference would be 52, leading to a new term of 114 + 52 = 166. Therefore, the next term in the sequence is 166.
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 for 4 10 18 28 40?
To find the nth term of the sequence 4, 10, 18, 28, 40, we first identify the pattern in the differences between consecutive terms: 6, 8, 10, and 12. The second differences are constant at 2, indicating a quadratic sequence. The nth term can be expressed as ( a_n = n^2 + n + 2 ). Thus, the nth term of the sequence is ( n^2 + n + 2 ).
What is the 10 term of the sequence 3 5 7 9?
The sequence provided is an arithmetic sequence where the first term is 3 and the common difference is 2. The formula for the nth term of an arithmetic sequence is given by ( a_n = a_1 + (n-1)d ), where ( a_1 ) is the first term and ( d ) is the common difference. For the 10th term, ( a_{10} = 3 + (10-1) \times 2 = 3 + 18 = 21 ). Thus, the 10th term of the sequence is 21.
What is the nth term for 98 94 90 84?
The nth term is -4n+102. Method: To find the nth term (Tn) of the sequence, multiply n by the pattern of change in the sequence from left to right (-4). Then, substitute n for a term, for example, term 2. Follow the first step (-4n) which will give -8. Then you add or subtract to equal the number of that term (94). -8+x=94. x=102. Therefore, the formula for the nth term is -4n+102. To prove it, try with any term. Term 3 (the number is 90). 3 x -4 = -12 -12 + 102 = 90 Tada!
What is the nth term for 3 11 21 33 47 63?
To find the pattern in the sequence 3, 11, 21, 33, 47, 63, we first need to calculate the differences between consecutive terms: 8, 10, 12, 14, 16. We notice that the differences are increasing by 2 each time. This indicates a quadratic relationship. By finding the second differences (which are constant at 2), we can conclude that the sequence follows a quadratic equation of the form an^2 + bn + c. Therefore, the nth term for this sequence is given by the quadratic equation an^2 + bn + c, where a = 1, b = 2, and c = 0.
What is the nth term of the quadratic sequence 5 20 45 80 125?
{5, 20, 45, 80, 125} = 5{1, 4, 9, 16, 25} = 5{1², 2², 3², 4², 5²} → U{n} = 5n²
What is the sequence if the nth term is 10 - 3n?
7
What is the nth term for 11 21 31 41?
10n + 1
What is the nth term of the sequence 15 25 35 45 55?
15(1)
What is the nth term in this sequence 11 21 35 53 75 101?
To find the nth term of the sequence 11, 21, 35, 53, 75, 101, we can observe the differences between consecutive terms: 10, 14, 18, 22, and 26, which increase by 4 each time. This suggests that the sequence can be described by a quadratic function. The nth term can be represented as ( a_n = 5n^2 + 6n ), where n starts from 1. Thus, the nth term corresponds to this formula for values of n.
What is the nth term of -2-8-18-32-50?
The sequence given is -2, -8, -18, -32, -50. To find the nth term, we first observe the differences between consecutive terms: -6, -10, -14, -18, which show that the second differences are constant at -4. This indicates that the nth term can be expressed as a quadratic function. By fitting the sequence to the form ( a_n = An^2 + Bn + C ), we find that the nth term is ( a_n = -2n^2 + 2n - 2 ).
