t{n} = (3n⁵ - 45n⁴ + 255n³ - 675n² + 1022n - 240)/40
This gives t{1..5} = {8, 13, 18, 23, 28}
and continues t{6...} = {42, 92, 232, 552, 1187, ...}
However, your teacher probably wants the much simpler:
t{n} = 5n + 3
Which also gives t{1..5} = {8, 13, 18, 23, 28}
but continues t{6...} = {33, 38, 43, 48, ...}
There are infinitely many formulae that can be given to give the terms t{1..5} = {8, 13, 18, 23, 28}; they all differ in what terms follow.
Which means that any formula for the nth term of t{1..5} = {8, 13, 18, 23, 28} is ONLY valid for n = 1, 2, ..., 5 as 5 terms have been given.
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Un = 5n - 2
The 'n'th term is [ 13 + 5n ].
The 'n'th term is [ 13 + 5n ].
It is: 10n-7 and so the next term is 43
35 * * * * * That is the next term. The question, however, is about the nth term. And that is 6*n - 1