Question

How do you find nth term rule for `375,-75,15,-3,....`?

Answer 1

`a_n=375 *(-1/5)^(n-1)`

Explanation:

Find the nth term rule for: `375, -75, 15, -3`...

If you divide any term by the previous term, the quotient is `-1/5`

This indicates the sequence is geometric. In other words, the next term is generated by multiplying the previous term by a fixed number called the common ratio or `r`.

The "formula" for a geometric sequence is `a_n=a_1 * r^(n-1)` where `r` is the common ratio, `a_1` is the first term in the sequence, and `n` is the number of the term in the sequence.

In this example, `r= -1/5` and `a_1 = 375`

`=> a_n=375 *(-1/5)^(n-1)`