2. Seats in 100th Row = 813
3. Rule is: [tex]a_n = 6*3^{n-1}[/tex]
Step-by-step explanation:
2. 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:
[tex]a_n = a_1 + (n-1)d\\[/tex]
Putting the values of a1 and d
[tex]a_n = 21 + (n-1)(8)\\a_n = 21 + 8n-8\\a_n = 13+8n[/tex]
for 100th row,
Putting n=100
[tex]a_{100} = 13+8(100)\\= 13 + 800\\= 813[/tex]
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
[tex]r = \frac{a_2}{a_1} = \frac{18}{6} = 3\\r = \frac{a_3}{a_2} = \frac{54}{18} = 3[/tex]
The given sequence is a geometric sequence as r is same for consecutive terms
The geometric sequence is given by:
[tex]a_n = a_1 . r^{n-1}\\a_n = 6 * 3^{n-1}[/tex]
Hence,
2. Seats in 100th Row = 813
3. Rule is: [tex]a_n = 6*3^{n-1}[/tex]
Keywords: Sequence, ratio
Learn more about sequences at:
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