Week 1 – My Arthmetic Sequence (Updated)

This week in Pre-Calculus 11 I learned about sequences and series and the differences between them.

My Arthmetic sequence is:

16, 4, -8, -20, -32, …

In this sequence we know,

$t_1=16$
d = -12 (the sequence decreases by 12 every time)
n = 5 (five is the last known term of the sequence)
$t_n=-32$

Pt. 1

To find the last number of a sequence ( $t_n$ ) a general formula ( $t_n=t_1+(n-1)d$ ) can be altered and simplified to suit my sequence:

$t_n=16+(n-1)(-12)$

$t_n=-12n+28$

So, if we were trying to find the 50th term ( $t_{50}$ ) we would just use the above formula and input all of the information that we know: n = 50 / d = -12/ $t_1=16$

$t_n=-12n+28$
$t_{50}=-12(50)+28$
$t_{50}=-600+28$
$t_{50}=-572$

Pt. 2

If we wanted to find the sum of the first 50 terms we would use one of the following formulas depending on what information is known:

$S_n=\frac{n}{2}(t_1+t_n)$ OR $S_n=\frac{n}{2}(t_1+t_1+(n-1)d)$ OR $S_n=\frac{n}{2}(2t_1+(n-1)d)$

After picking an appropriate formula you input all the information that you know into it:

we know: n = 50 / $t_1=16$ / $t_{50}=-572$

$S_n=\frac{n}{2}(t_1+t_n)$
$S_{50}=\frac{50}{2}(16 -32)$
$S_{50}= 25 (-16)$
$S_{50}=-400$

M	T	W	T	F	S	S
			1	2	3	4
5	6	7	8	9	10	11
12	13	14	15	16	17	18
19	20	21	22	23	24	25
26	27	28

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Week 1 – My Arthmetic Sequence (Updated)

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