Question

Write an explicit formula for the arithmetic sequence whose common difference is -2.5

Answer 1

an arithmetic sequence is just a sequence in which every term has the same difference, like 2, 4, 6, 8, 10... the common difference here is 2.
you could even use 2, -5, -12, -19, because the common difference is -7

Answer 2

for an explicit formula you can't include a reference to any other numbers in the sequence, so that plugging in any number to the equation will get us the term we want.
so the only question now is, how do we make the common difference -2.5?

Answer 3

whelp, we can use many, many formulas for this (in fact there are an infinite number of equations for this), but let's start with the most basic one.
$$a_n = -2.5n$$

Answer 4

this works because for any n we have, \(a_{n-1}\) and \(a_{n+1}\) will be 2.5 away from \(a_n\)

Answer 5

we can also add any number to this sequence and it'll still work. e.g.
$$a_n = 5 - 2.5n$$
the common difference still stands

Answer 6

marry me :DDD

Answer 7

LMAO