Oh, what a beautiful sequence of numbers you've created! To find the pattern, we can see that each number is increasing by adding consecutive odd numbers. The nth term for this sequence can be found using the formula n^2 + n. Just like painting, sometimes all we need is a little patience and observation to uncover the hidden beauty within patterns.
The given sequence 0, 3, 8, 15, 24 is an arithmetic sequence where the nth term is given by the formula (a_n = a_1 + (n-1)d), where (a_1) is the first term, (d) is the common difference, and (n) is the term number. To find the nth term, we need to first identify the common difference between consecutive terms. The common difference in this sequence is 3, 5, 7, 9, which increases by 2 each time. Therefore, the nth term for this sequence is (a_n = 0 + (n-1)2 = 2n - 2).
To find the nth term of a sequence, we first need to identify the pattern or rule that governs the sequence. In this case, the sequence is decreasing by 6 each time. Therefore, the nth term can be represented by the formula: 18 - 6(n-1), where n is the position of the term in the sequence.
The given sequence is an arithmetic sequence with a common difference of 5. To find the nth term of an arithmetic sequence, we use the formula: (a_n = a_1 + (n-1)d), where (a_n) is the nth term, (a_1) is the first term, (n) is the term number, and (d) is the common difference. In this case, the first term (a_1 = 0) and the common difference (d = 5). Therefore, the nth term of the sequence is (a_n = 0 + (n-1)5 = 5n - 5).
The given sequence appears to be increasing by 10 each time. To find the nth term, we can use the formula for arithmetic sequences: nth term = first term + (n-1) * common difference. In this case, the first term is 4 and the common difference is 10. Therefore, the nth term for this sequence would be 4 + (n-1) * 10, which simplifies to 10n - 6.
An = 2(n - 1)2 + 2(n - 1) = 2n(n - 1)
16 - 4nor4 (4 - n)
Well, darling, the nth term for the sequence 18, 12, 6, 0, -6 is -6n + 24. So, if you plug in n = 1, you get 18; n = 2 gives you 12, and so on. Just a little math magic for you to enjoy!
To find the nth term of a sequence, we first need to identify the pattern or rule that governs the sequence. In this case, the sequence is decreasing by 6 each time. Therefore, the nth term can be represented by the formula: 18 - 6(n-1), where n is the position of the term in the sequence.
0
The given sequence is an arithmetic sequence with a common difference of 5. To find the nth term of an arithmetic sequence, we use the formula: (a_n = a_1 + (n-1)d), where (a_n) is the nth term, (a_1) is the first term, (n) is the term number, and (d) is the common difference. In this case, the first term (a_1 = 0) and the common difference (d = 5). Therefore, the nth term of the sequence is (a_n = 0 + (n-1)5 = 5n - 5).
n - 1
7 - 4n where n denotes the nth term and n starting with 0
If the nth term is 8 -2n then the 1st four terms are 6, 4, 2, 0 and -32 is the 20th term number
To find the nth term of a sequence, we first need to identify the pattern or rule governing the sequence. In this case, the sequence appears to be increasing by 9, then 13, then 17, and so on. This pattern indicates that the nth term is given by the formula n^2 + n - 1. So, the nth term of the sequence 0, 9, 22, 39, 60 is n^2 + n - 1.
n-9+3
The given sequence appears to be increasing by 10 each time. To find the nth term, we can use the formula for arithmetic sequences: nth term = first term + (n-1) * common difference. In this case, the first term is 4 and the common difference is 10. Therefore, the nth term for this sequence would be 4 + (n-1) * 10, which simplifies to 10n - 6.
An = 2(n - 1)2 + 2(n - 1) = 2n(n - 1)
This is the Fibonacci sequence, where the number is the sum of the two preceding numbers. The nth term is the (n-1)th term added to (n-2)th term