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)
A1 = first term
a1 = 15
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d = common difference
d = (second term) - (first term)
d = a2 - a1
d = 9-12
d = -3
The negative common difference indicates that the terms are decreasing
Each time we subtract 3, or add -3, to get the next term.
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nth term of arithmetic sequence
an = a1 + d(n-1)
an = 15 + (-3)(n-1)
an = 15- 3n + 3
an = 18 - 3n
Answer is choice D
Answer: The system of inequalities would be,
x + y ≤ 130, x > 0.25y, x ≥ 0, y ≥0
Step-by-step explanation:
Here, x represents the amount to be planted in tomatoes and y represents the amount to be planted in cucumbers, ( in square ft )
Thus, the total area required ( in square ft )= x + y
Since, the available area = 130 ft²,
⇒ Total area ≤ 130 ft²
⇒ x + y ≤ 130,
∵ the area planted with tomatoes to be more than 25% of the area planet with cucumbers,
⇒ x > 25% of y
⇒ x > 0.25y
Also, area can not be negative,
⇒ x ≥ 0, y ≥ 0
Statement #3 is incorrect. The actual ratio is 1/15. The rest of the statements are true.
Answer: 3/2 acre per day
Explanation:
8 1/4 = 33/4
5 1/2 = 11/2
Find the unit rate in acre per day:
(33/4) divide by (11/2)
33/4 x 2/11 = 3/2
