According to Wittgenstein's Finite Rule Paradox every finite sequence of numbers can be a described in infinitely many ways and so can be continued any of these ways - some simple, some complicated but all equally valid.
The simplest quadratic function, in this case, is U(9) = n^2 + 9 for n = 1, 2, 3, ...
The sequence has a difference of 10, so the nth term starts with 10n. Then to get to -8 from 10 you need to subtract 18. So the nth term is 10n - 18.
Un = 5n - 2
The nth term in this arithmetic sequence is an=26+(n-1)(-8).
The 'n'th term is [ 13 + 5n ].
The 'n'th term is [ 13 + 5n ].
The sequence has a difference of 10, so the nth term starts with 10n. Then to get to -8 from 10 you need to subtract 18. So the nth term is 10n - 18.
Un = 5n - 2
The nth term in this arithmetic sequence is an=26+(n-1)(-8).
The 'n'th term is [ 13 + 5n ].
The 'n'th term is [ 13 + 5n ].
It is: 5n+3 and so the next term is 28
The 'n'th term is [ 13 + 5n ].
1,7,13,19
It is: 25-7n
The next term is 45 because the numbers are increasing by increments of 3 5 7 9 and then 11
tn = n2 + 9, n = 1,2,3,...
Well, isn't that just a lovely pattern we have here? Each term is increasing by 4, isn't that delightful? So, if we want to find the nth term, we can use the formula: nth term = first term + (n-1) * common difference. Just like painting a happy little tree, we can plug in the values and find the nth term with ease.