The correct answer is B because the data points are too scattered
Hope this helped :)
Part A
Answer: The common ratio is -2
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Explanation:
To get the common ratio r, we divide any term by the previous one
One example:
r = common ratio
r = (second term)/(first term)
r = (-2)/(1)
r = -2
Another example:
r = common ratio
r = (third term)/(second term)
r = (4)/(-2)
r = -2
and we get the same common ratio every time
Side Note: each term is multiplied by -2 to get the next term
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Part B
Answer:
The rule for the sequence is
a(n) = (-2)^(n-1)
where n starts at n = 1
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Explanation:
Recall that any geometric sequence has the nth term
a(n) = a*(r)^(n-1)
where the 'a' on the right side is the first term and r is the common ratio
The first term given to use is a = 1 and the common ratio found in part A above was r = -2
So,
a(n) = a*(r)^(n-1)
a(n) = 1*(-2)^(n-1)
a(n) = (-2)^(n-1)
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Part C
Answer: The next three terms are 16, -32, 64
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Explanation:
We can simply multiply each previous term by -2 to get the next term. Do this three times to generate the next three terms
-8*(-2) = 16
16*(-2) = -32
-32*(-2) = 64
showing that the next three terms are 16, -32, and 64
An alternative is to use the formula found in part B
Plug in n = 5 to find the fifth term
a(n) = (-2)^(n-1)
a(5) = (-2)^(5-1)
a(5) = (-2)^(4)
a(5) = 16 .... which matches with what we got earlier
Then plug in n = 6
a(n) = (-2)^(n-1)
a(6) = (-2)^(6-1)
a(6) = (-2)^(5)
a(6) = -32 .... which matches with what we got earlier
Then plug in n = 7
a(n) = (-2)^(n-1)
a(7) = (-2)^(7-1)
a(7) = (-2)^(6)
a(7) = 64 .... which matches with what we got earlier
while the second method takes a bit more work, its handy for when you want to find terms beyond the given sequence (eg: the 28th term)
Answer:
x=9
Step-by-step explanation:
−4(4−x)=4/5(x+16)
(−4)(4)+(−4)(−x)=(4/5)(x)+(4/5)(16)(Distribute)
−16+4x=4/5x+64/5
4x−16=4/5x+64/5
4x−16−4/5x=4/5x+64/5−4/5x
16/5x−16=64/5
16/5x−16+16=64/5+16
16/5x=144/5
(5/16)*(16/5x)=(5/16)*(144/5)
x=9
hopfully this helps answer: x=9
Answer:
(-1, -3)
Step-by-step explanation:
The midpoint coordinates are the average of the respective end point coordinates:
M = (P +Q)/2
M = ((-7, 1) +(5, -7))/2 = (-7+5, 1-7)/2 = (-2, -6)/2
M = (-1, -3) . . . . the midpoint of PQ
