Question

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

Answer 1

Answer:

-56.3

Step-by-step 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:

$a_{28}=5.8+-2.3(28-1)$

$a_{28}=5.8+-2.3(27)$

$a_{28}=-56.3$