## Week 2 Pre Calc 11

This week I learned about Finite geometric series, I learned how to find $t_n$ and I also learned how to find the sum of $t_1$ to $t_n$.

To find $t_n$ you need $t_1$ and the common ratio.

So say I was trying to find $t_(15)$, so $t_1$=4 and the common ratio is 3. This is what you would do.

Then to find the sum of all the 15 t’s, you would add $t_1$ + $t_2$ + $t_3$ +…etc. But the easier way to do it would be to do this.

## My arithmetic sequence

$t_1$ = 3, $t_2$ = 10, $t_3$ = 17, $t_4$ = 24, $t_5$ = 31.

So 3, 10, 17, 24, 31…

$t_{50}$?   $S_{50}$?

what I would do first is find out what is $t_{50}$.

$t_n$=$t_1$+(n-1)d

$t_{50}$=3+49(7)

$t_{50}$=3+343

$t_{50}$=346

Now I need to find $S_50$.

$S_n$=$\frac{n}{2}$($t_1$+$t_{50}$)

$S_{50}$=$\frac{50}{2}$(3+346)

$S_{50}$=25(349)

$S_{50}$=8725

So $t_{50}$=346 and $S_{50}$=8725.

## Week 1 Pre Calc 11

This short week we learned about sequences but more importantly we learned how to get whatever number from the sequence.

Basically if $t_1$ was 5, then $t_2$ was 10, and $t_3$ then with what we learned I could find out what was $t_{45}$.

this is how.

This is what I learned this past week!