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1 answer:
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(a) The explicit rule to model the sequence formed by the number of seats in each row is
(b) The 35th row has 120 seats
Step-by-step explanation:
The rule of the nth term of an arithmetic sequence is
, where
- a is the the first term
- d is the common difference between each two consecutive terms
∵ There are 18 seats in the 1st row
∵ There are 21 seats in the 2nd row
∵ 21 - 18 = 3
∵ The number of seats is increased by 3 with each additional row
- The number of seats in each row represents an arithmetic
sequence because there is a common difference between
each two consecutive rows
∴ The number of seats in each row formed an arithmetic sequence
∵ The number of seats in the first row = 18 seats
∴ a = 18
∵ The number of seats in a row continues to increase by 3 with each
additional row
∴ d = 3
- Substitute the values of a and d in the rule of nth term
∴
- Simplify the right hand side
∴
- Add like terms
∴
(a) The explicit rule to model the sequence formed by the number of seats in each row is
∵ There are 120 seat in a row
- Substitute by 120 in the rule above
∴ 120 = 15 + 3n
- Subtract 15 from both sides
∴ 105 = 3n
- Divide both sides by 3
∴ n = 35
∴ The number of the row is 35
(b) The 35th row has 120 seats
Learn more:
You can learn more about the sequences in brainly.com/question/7221312
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Answer:
40 students
Step-by-step explanation:
In this problem, one is given the ratio ( 8 : 3 ), since a ratio is another way of writing a fraction one can rewrite it as; (8) represent the number of students who want to learn about magnets, and (3) represents the number of students who want to learn about magic tricks.
In the problem, it is also given that 25 more students wanted to learn about magnets compared to magic tricks. If one uses the parameter (x) to represent the factor by which the fraction is reduced, then one can get the equation;
8x = 3x + 25
Use inverse operations to solve,
8x = 3x + 25
-3x
5x = 25
/5
x = 5
Substitute back in to find out how many students want to learn about magnets,
8x
= 8(5)
= 40