Week 1 – Arithmetic Sequences

For the first week of Pre-Calculus 11 we learned about Arithmetic Sequences.

My arithmetic sequence is 97, 84, 71, 58, 45…

$d=-13$

How to find $t_{50}$ :

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

$t_{50}=97+(50-1)(-13)$

$t_{50}=97+(49)(-13)$

$t_{50}=97+-637$

$t_{50}=-540$

General equation for $t_n$ :

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

$t_n=97+(n-1)(-13)$

$t_n=97+-13n+13$

$t_n=-13n+110$

How to find $S_{n}$ :

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

$S_{50}=\frac{50}{2}(97+-540)$

$S_{50}=25(-443)$

$S_{50}=-11,075$

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