What is the total volume of glass used to make the award?
2 answers:
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Answer:
Option D. 13122 is the answer.
Step-by-step explanation:
As we can see from the table having interval and average rate of change, figures under average rate of change are forming a geometric sequence.
Sequence is 2, 6, 18 , 54, 162, 486.
and we have to find the average rate of change from x = 8 to x = 9, means we have to find 9th term of the given sequence.
Now we know that explicit formula of the sequence can be written as
where Tn is the nth term of the sequence.
a = first term
r = common ratio
n = number of the term
Now from this explicit formula we can find the 9th term of the sequence.
From the given table
a = 2, r = 3, n = 9
T9 = 13122
Therefore Option D. 13122 will be the answer.
The value of d is -2
Step-by-step explanation:
The nth term of the arithmetic sequence is , where
is the first term
- d is the common difference between each 2 consecutive terms
The nth term of the geometric sequence is , where
- r is the common ratio between each two consecutive terms
∵ of an arithmetic sequence is 1
∵ The common difference is d, where d ≠ 0
∵ ,
,
are the first 3 terms of a geometric sequence
∵ = 1 + (2 - 1)d
∴ = 1 + d
∵ = 1 + (3 - 1)d
∴ = 1 + 2d
∵ = 1 + (6 - 1)d
∴ = 1 + 5d
∴ The first 3 terms of the geometric sequence are (1 + d) , (1 + 2d) ,
(1 + 5d)
∵ The common ratio in the geometric sequence is
∴
- Use cross multiplication with the equal fractions
∵
∴ (1 + 2d)(1 + 2d) = (1 + d)(1 + 5d)
∴ 1 + 2d + 2d + 4d² = 1 + 5d + d + 5d²
- Add like terms in each side
∴ 1 + 4d + 4d² = 1 + 6d + 5d²
- Subtract 1 from both sides
∴ 4d + 4d² = 6d + 5d²
- Subtract 4d from both sides
∴ 4d² = 2d + 5d²
- Subtract 4d² from each side
∴ 0 = 2d + d²
- Take d as a common factor
∴ 0 = d(2 + d)
- Equate each factor by 0
∴ d = 0 but we will reject it because d ≠ 0
∴ 2 + d = 0
- Subtract 2 from both sides
∴ d = -2
The value of d is -2
Learn more:
You can learn more about the sequence in brainly.com/question/1522572
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