The table below shows the relationship between the number of roller coasters at the fair in the amount the fair which shows the
1 answer:
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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
#LearnwithBrainly
Answer:
The answer is below
Step-by-step explanation:
The equation of a linear function is given as:
y = mx + b;
where y, x are variables, m is the rate of change and b is the initial value of variable y.
A) Since there is B bacteria in the Petri dish at 12:00 midnight and the number of bacteria increases after midnight by 25 every hour. Let h represent the time in hours and T represent the total number of bacteria, therefore the equation is:
T = 25h + B
B) Given that B = 5, h = 6, hence:
T = 25(6) + 5 = 150 + 5 = 155 bacteria
C) The equation of the graph is:
T = 25h + 5
The graph was plotted using geogebra online graphing.
