Since each number is 2 less than the previous number, the formula that comes to mind immediately is -2n. However, since the first number is 2 instead of -2, an additional adjustment is required. This can be done by adding 4 to each term. The result is:4-2n
equivalent to:
2(2-n)
multiplies by 2
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.
The sequence 4, 6, 8, 10 is an arithmetic sequence where each term increases by 2. The nth term formula can be expressed as ( a_n = 4 + (n - 1) \cdot 2 ). Simplifying this gives ( a_n = 2n + 2 ). Thus, the nth term of the sequence is ( 2n + 2 ).
The nth term of the sequence given by the formula (2 - n) can be found by substituting (n) with the first three positive integers: For (n = 1): (2 - 1 = 1) For (n = 2): (2 - 2 = 0) For (n = 3): (2 - 3 = -1) Thus, the first three terms of the sequence are 1, 0, and -1.
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 4, then 8, then 12, then 16, and so on. This pattern suggests that the nth term can be represented by the formula n^2 + n, where n is the position of the term in the sequence. So, the nth term for the given sequence is n^2 + n.
multiplies by 2
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.
2(n-1)
The sequence 4, 6, 8, 10 is an arithmetic sequence where each term increases by 2. The nth term formula can be expressed as ( a_n = 4 + (n - 1) \cdot 2 ). Simplifying this gives ( a_n = 2n + 2 ). Thus, the nth term of the sequence is ( 2n + 2 ).
The nth term of the sequence given by the formula (2 - n) can be found by substituting (n) with the first three positive integers: For (n = 1): (2 - 1 = 1) For (n = 2): (2 - 2 = 0) For (n = 3): (2 - 3 = -1) Thus, the first three terms of the sequence are 1, 0, and -1.
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 4, then 8, then 12, then 16, and so on. This pattern suggests that the nth term can be represented by the formula n^2 + n, where n is the position of the term in the sequence. So, the nth term for the given sequence is n^2 + n.
To find the nth term of the sequence 0, 3, 8, 15, 24, 35, we can observe the pattern in the differences between consecutive terms. The differences are 3, 5, 7, 9, 11, which form an arithmetic sequence with a common difference of 2. This suggests that the nth term can be represented by the formula ( n^2 - n ), where n starts from 1. Thus, the nth term for the given sequence is ( n^2 - n ).
If 3 is the first term, then the nth term is [ 3 x 2(n-1) ] .
The given sequence is -2, -4, -6, which is an arithmetic sequence where each term decreases by 2. The first term (a) is -2, and the common difference (d) is -2. The nth term can be expressed using the formula ( a_n = a + (n-1)d ). Thus, the nth term is given by ( a_n = -2 + (n-1)(-2) = -2n ).
n - 1
If 3 is the first term, then the nth term is [ 3 x 2(n-1) ] .
To find the nth term formula for the sequence -4, -1, 4, 11, 20, 31, we first observe the differences between consecutive terms: 3, 5, 7, 9, 11, which are increasing by 2. This indicates a quadratic relationship. The nth term formula can be derived as ( a_n = n^2 + n - 4 ).