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photoshop1234 [79]
3 years ago
10

Help me with this test in math please!! (questions in images)

Mathematics
2 answers:
irga5000 [103]3 years ago
8 0

Answer:

0

Step-by-step explanation:

There is no slope because it is a strait vertical line.

gogolik [260]3 years ago
3 0
1. Positive
2. Undefined
3. Negative
4. Zero
5. 4/3
6. 3/1
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Find an for the arithmetic series with s16 = -288 And a1 =-21
Maru [420]
If d is the common difference between terms in the sequence \{a_n\}, then

a_1=-21
a_2=a_1+d=-21+d
a_3=a_2+d=-21+2d
...
a_n=a_{n-1}+d=\cdots=-21+(n-1)d

You're told that S_{16}=-288 (the sum of the first 16 terms in the sequence, presumably). Well, we know that

S_{16}=\displaystyle\sum_{n=1}^{16}a_n=\sum_{n=1}^{16}(-21+(n-1)d)
S_{16}=\displaystyle(-21-d)\sum_{n=1}^{16}1+d\sum_{n=1}^{16}n

Recall that

\displaystyle\sum_{n=1}^kn=\frac{k(k+1)}2

so that we have

-288=16(-21-d)+\dfrac{16(16+1)}2d\implies d=\dfrac25

So we get

\begin{cases}a_1=-21\\\\a_n=-21+\dfrac25(n-1)\end{cases}
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