Question

Find a28 in the arithmetic sequence: 5.8, 3.5, 1.2, -1.1,

Answer 1

-56.3

Explanation:

We don't have to much guessing because it tells us it is arithmetic which means it has a common difference.

That is a term minus it's previous will be the same.

`3.5-5.8=-2.3`

`1.2-3.5=-2.3`

`-1.1-1.2=-2.3`

In general:

`a_n-a_(n-1)=-2.3` with
`a_1=5.8` if you wanted the recursive form.

You can also find the explicit form which would be more helpful for our task of finding the 28th term.

`a_n=a_1+d(n-1)` is the explicit form where
`d` is the common difference and
`a_1` is the first term.

Inputting -2.3 for
`d` and 5.8 for
`a_1`:

`a_n=5.8+-2.3(n-1)`

Now the 28th term or
`a_(28)` can be found by replacing n with 28:

`a_(28)=5.8+-2.3(28-1)`

`a_(28)=5.8+-2.3(27)`

`a_(28)=-56.3`