To find the nth term of a sequence, we need to identify the pattern between the numbers. Looking at the differences between consecutive terms, we see that the differences are increasing by 9, 15, 21, and so on. This indicates that the sequence is following a pattern of adding consecutive odd numbers (1, 3, 5, 7, ...). Therefore, the nth term of this sequence can be expressed as n^2 + 7.
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I can tell you that it is increasing 9, 15, 21, 27. i.e. adding on 6 to the gap each time so if you mean the next term by nth term, then it will be adding on 33, which will leave you at 113
t(n) = 12*n + 5
To find the term number when the term value is 53 in a sequence, you need to know the pattern or formula of the sequence. If it is an arithmetic sequence with a common difference of d, you can use the formula for the nth term of an arithmetic sequence: ( a_n = a_1 + (n-1)d ), where ( a_n ) is the nth term, ( a_1 ) is the first term, and d is the common difference. By plugging in the values, you can solve for the term number.
tn = 2x2 + 3 where x = 1, 2, 3, ...
12 + 32 + 53 = 97
n=n3. The numbers given in the question are equal to 13, 23, 33, 43, 53.