Question

WILL GIVE 100 POINTS



1. In a music stadium, there are 18 seats in the first row and 21 seats in the second row. The number of seats in a row continues to increase by 3 with each additional row.

(a) Write an explicit rule to model the sequence formed by the number of seats in each row. Show your work.

(b) Use the rule to determine which row has 120 seats. Show your work.

Answer 1

(a) The explicit rule to model the sequence formed by the number of seats in each row is $a_{n}=15+3n$

(b) The 35th row has 120 seats

Step-by-step explanation:

The rule of the nth term of an arithmetic sequence is

$a_{n}=a+(n-1)d$ , 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

∴ $a_{n}=18+(n-1)3$

- Simplify the right hand side

∴ $a_{n}=18+3n-3$

- Add like terms

∴ $a_{n}=15+3n$

(a) The explicit rule to model the sequence formed by the number of seats in each row is $a_{n}=15+3n$

∵ There are 120 seat in a row

- Substitute $a_{n}$ 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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