The sequence 11, 21, 35, 53, 75, 101 can be analyzed to find a pattern in the differences between consecutive terms: 10, 14, 18, 22, 26. The differences themselves increase by 4 each time, indicating a quadratic relationship. The nth term can be expressed by the formula ( a_n = 3n^2 + 8n ), where ( n ) is the term number starting from 1. For example, for ( n = 1 ), ( a_1 = 11 ), and for ( n = 2 ), ( a_2 = 21 ).
The given sequence is 11, 31, 51, 72 The nth term of this sequence can be expressed as an = 11 + (n - 1) × 20 Therefore, the nth term is 11 + (n - 1) × 20, where n is the position of the term in the sequence.
One of the infinitely many possible rules for the nth term of the sequence is t(n) = 4n - 1
The nth term in the sequence -5, -7, -9, -11, -13 can be represented by the formula a_n = -2n - 3, where n is the position of the term in the sequence. In this case, the common difference between each term is -2, indicating a linear sequence. By substituting the position n into the formula, you can find the value of the nth term in the sequence.
The 'n'th term is [ 4 - 3n ].
Double it minus the previous number.
The given sequence is 11, 31, 51, 72 The nth term of this sequence can be expressed as an = 11 + (n - 1) × 20 Therefore, the nth term is 11 + (n - 1) × 20, where n is the position of the term in the sequence.
The nth term in this sequence is 4n + 3.
The nth term of the sequence is 2n + 1.
One of the infinitely many possible rules for the nth term of the sequence is t(n) = 4n - 1
The nth term in the sequence -5, -7, -9, -11, -13 can be represented by the formula a_n = -2n - 3, where n is the position of the term in the sequence. In this case, the common difference between each term is -2, indicating a linear sequence. By substituting the position n into the formula, you can find the value of the nth term in the sequence.
The nth term is 4n-1 and so the next term will be 19
3 11
The nth term of the sequence is (n + 1)2 + 2.
10n + 1
The given sequence is an arithmetic sequence with a common difference of 7 (18-11=7, 25-18=7, and so on). To find the nth term of an arithmetic sequence, you can 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 position of the term, and d is the common difference. In this case, the first term a_1 is 11 and the common difference d is 7. So, the nth term of this sequence is 11 + (n-1)7, which simplifies to 11 + 7n - 7, or 7n + 4.
The 'n'th term is [ 4 - 3n ].
The 'n'th term is [ 4 - 3n ].