What is the nth term of 8 13 18 23 28?

Answer 1

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.