Question

How do you find the formula for `a_n` for the arithmetic sequence `4, 3/2, -1, -7/2,...`?

Answer 1

If the initial term is `a_0 =4` then `a_n=4-5/2n`
If the initial term is `a_1=4` then `a_n=4-(5 * (n-1))`

Explanation:

This appears to be an arithmetic sequence (and the question was asked under the heading Arithmetic Sequences)
Checking the difference between successive terms we see that
`color(white)("XXX")a_(i+1)=a_i - 5/2`
That is the initial value is reduced by a further `5/2` for each successive term.

When I learned this stuff (many years ago), the initial term was denoted `a_0`.
It seems that `a_1` is now a more common designation for that first term (at least that is what I think I am seeing on this site)