Question 1) In an auditorium, there are 22 seats in the first row and 28 seats in the second row. The number of seats in a row continues to increase by 6 with each additional row. A) Write an iterative 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 100 seats. Show your work. ( No Plagiarism and only answer if you know how to work this problem out. Will Mark Brainliest).

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Step-by-step explanation

In an auditorium, there are 21 seats in the first row and 29 seats in the second row. The number of seats in a row continues to increase by 8 with each additional row. How would you find the 100th row?

We can take this as an arithmetic sequence, as the seats in next row is calculated by adding 8 to previous row

So here common difference will be 8

the first term is 21

the arithmetic sequence is given by:

Putting the values of a1 and d

for 100th row,

Putting n=100

3. The sequence 6, 18, 54, 162, … shows the number of pushups Kendall did each week, starting with her first week of exercising.

Give the rule you would use to find the 20th week.

Given sequence is:

6, 18, 54, 162, …

we can see that the common difference is not same so we will find the common ratio

The given sequence is a geometric sequence as are the same for consecutive terms

The geometric sequence is given by:

Hence,

2. Seats in 100th Row = 813

3. Rule is:

Keywords: Sequence, ratio

see explanation

Step-by-step explanation:

The sequence is

22, 28, 34, ....

Since there is a common difference of 6 the sequence is arithmetic with n th term

= a₁ + (n - 1)d

a₁ is the first term and d the common difference

Here a₁ = 22 and d = 6, then

= 22 + 6(n - 1) = 22 + 6n - 6 = 6n + 16

Equate to 100 and solve for n

6n + 16 = 100 ( subtract 16 from both sides )

6n = 84 ( divide both sides by 6 )

n = 14

Thus the 14 th row has 100 seats