Question

WILL GIVE 100 POINTS

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

#LearnwithBrainly