(n(n-1) divided by 2 + 1) multiplied by 3) +6
There is no pattern
12, 8
The sequence 6, 13, 20, 27 increases by 7 each time. This indicates it is an arithmetic sequence with a common difference of 7. The nth term can be expressed as ( a_n = 6 + 7(n-1) ), which simplifies to ( a_n = 7n - 1 ). Thus, the nth term is ( 7n - 1 ).
The sequence 13, 20, 27, 34, 41 is an arithmetic sequence with a common difference of 7. The nth term formula can be expressed as ( a_n = 13 + (n - 1) \times 7 ). Simplifying this, we get ( a_n = 7n + 6 ). Thus, the nth term is given by ( a_n = 7n + 6 ).
tn = 3n or 3*3* ... *3 (where there are n threes.)
The nth term of the sequence is (n + 1)2 + 2.
The sequence 18, 27, 36, 45, 54 is an arithmetic sequence where each term increases by 9. To find the nth term, you can use the formula for the nth term of an arithmetic sequence: ( a_n = a_1 + (n-1)d ), where ( a_1 ) is the first term (18) and ( d ) is the common difference (9). Thus, the nth term is ( a_n = 18 + (n-1) \times 9 = 9n + 9 ).
5n+2
There is no pattern
Had it not been for 64, the nth term would be given by t(n) = 3*n2 However, this cannot be the case because then t(4) would have been 48, not 64.
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.
2n +29
Willies
n3
12, 8
The sequence 6, 13, 20, 27 increases by 7 each time. This indicates it is an arithmetic sequence with a common difference of 7. The nth term can be expressed as ( a_n = 6 + 7(n-1) ), which simplifies to ( a_n = 7n - 1 ). Thus, the nth term is ( 7n - 1 ).
3^n These are powers of 3