15(1)
The nth term is: 5n
The nth term is: 5-6n
n2
5^n
Divide the sequence by 5 and the answer becomes very obvious: 1, 4, 9, 16,...N2 So, 5, 20, 45, 80,...5N2
The nth term is: 5n
The nth term is: 5-6n
The sequence you provided seems inconsistent, as it starts with a decreasing pattern (15, 12, 9, 6) and then jumps to 25, which breaks the sequence. The first four terms decrease by 3 each time, but without a clear pattern for the fifth term. If you intended to continue the sequence in a specific way, please clarify, and I can help determine the nth term.
To determine the nth term of the sequence 25, 16, 7, we first identify the pattern. The sequence appears to be decreasing by 9, then by 9 again, suggesting a consistent difference. This leads to a formula for the nth term: ( a_n = 34 - 9n ), where ( a_1 = 25 ) for n=1. Thus, the nth term can be expressed as ( a_n = 34 - 9n ).
n2
It is 4n+5 and so the next term will be 25
5^n
Please note that (a) this is a sequence of square numbes, and (b) the sequence starts at 22.
Divide the sequence by 5 and the answer becomes very obvious: 1, 4, 9, 16,...N2 So, 5, 20, 45, 80,...5N2
The sequence given is an arithmetic sequence where each term increases by 6. 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 and ( d ) is the common difference. Here, ( a_1 = 7 ) and ( d = 6 ). Thus, the nth term can be expressed as ( a_n = 7 + (n-1) \times 6 = 6n + 1 ).
It is: 27-2n
t(n) = 28-3n where n = 1,2,3,...