Week 1 – Arithmetic Sequences

In week 1 of math class we learnt about arithmetic sequences and series.

My sequence is 6, 10, 14, 18, 22,…

To find $t_{50}$ you would use the formula, $t_n=t_1+(n-1)d$ Where $t_n$ is equal to term 50, $t_1$ is equal to 6, n-1 is equal to 49, and d is equal 4.

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

$t_{50}=6+(50-1)4$

$t_{50}=6+196$

$t_{50}=202$

To find $t_n$ you would use the same formula as above and keep it in the general form.

$t_n=6+(n-1)4$

$t_n=6+4n-4$

$t_n=2+4n$

$t_n=4n+2$ This formula can be used to find any term number in the sequence.

To find the sum of the first 50 terms you would use the following formula. $S_n=\frac{n}{2}(t_1+t_n)$

$S_{50}=\frac{50}{2}(6+202)$

$S_{50}=25(208)$

$S_{50}=5,200$

Week 1 – Arithmetic Sequences

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