### February 4th 2018 archive

4, 9, 14, 19, 24

$d=5$, $t_1=4$

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

$t_n=4+(n-1)5$

$t_n=4+5n-5$

$t_n=5n-1$

using this information, we can find any value of $t$ using the equation $t_n=5n-1$. We can plug in any term into $n$ to find $t_n$

this equation will work for any term within the sequence, as long as the starting term and common difference are constant. If either of these change it is no longer an arithmetic sequence.

To find $S_{50}$, the sum of all 50 terms, we must use the equation $S_n={n}{2}(a+1)$

In this equation, $n=$ number of terms(50) and $a=$ the first term(4)

$S_{50}={50}{2}(4+1)$

$S_{50}=25(5)$

$S_{50}=125$