One of the infinitely many possible rules for the nth term of the sequence is t(n) = 4n - 1
The sequence 3, 7, 11 is an arithmetic sequence where the first term is 3 and the common difference is 4. The nth term formula for an arithmetic sequence can be expressed as ( a_n = a_1 + (n - 1)d ), where ( a_1 ) is the first term and ( d ) is the common difference. Substituting the values, the nth term formula for this sequence is ( a_n = 3 + (n - 1) \cdot 4 ), which simplifies to ( a_n = 4n - 1 ).
The sequence 0, 3, 6, 9, 12 is an arithmetic sequence where the first term is 0 and the common difference is 3. The formula for the nth term can be expressed as ( a_n = 3(n - 1) ) or simply ( a_n = 3n - 3 ). This formula generates the nth term by multiplying the term's position (n) by 3 and adjusting for the starting point of the sequence.
The sequence 3, 8, 13, 18, 23, 28 increases by 5 each time. This indicates a linear pattern. The nth term can be expressed as ( a_n = 3 + 5(n - 1) ), which simplifies to ( a_n = 5n - 2 ). Thus, the nth term of the sequence is ( 5n - 2 ).
Strangely enough, it is 9n + 1 for n = 1, 2, 3, ...
The nth term of the sequence is 2n + 1.
The given sequence is an arithmetic sequence with a common difference of 4 between each term. To find the nth term of an arithmetic sequence, we use the formula: nth term = a + (n-1)d, where a is the first term, d is the common difference, and n is the term number. In this case, the first term (a) is -3, the common difference (d) is 4, and the term number (n) is the position in the sequence. So, the nth term of the given sequence is -3 + (n-1)4 = 4n - 7.
12 - 5(n-1)
One of the infinitely many possible rules for the nth term of the sequence is t(n) = 4n - 1
The nth term is 4n-1 and so the next term will be 19
Well, darling, it looks like we have a simple arithmetic sequence here. The common difference between each term is 1, so the nth term formula is just n + 3. So, if you want the nth term for 4 5 6 7 8, it's n + 3. Hope that clears things up for ya!
The given sequence is an arithmetic sequence with a common difference that increases by 1 with each term. To find the nth term of an arithmetic sequence, you can use the formula: nth term = a + (n-1)d, where a is the first term, n is the term number, and d is the common difference. In this case, the first term (a) is 3 and the common difference (d) is increasing by 1, so the nth term would be 3 + (n-1)(n-1) = n^2 + 2.
If 3 is the first term, then the nth term is [ 3 x 2(n-1) ] .
The nth term in this sequence is 4n + 3.
If 3 is the first term, then the nth term is [ 3 x 2(n-1) ] .
The nth term of a sequence is the general formula for a sequence. The nth term of this particular sequence would be n+3. This is because each step in the sequence is plus 3 higher than the previous step.
The nth term for that arithmetic progression is 4n-1. Therefore the next term (the fifth) in the sequence would be (4x5)-1 = 19.