Question

Please someone help! I've been struggling with this assignment! SHOW ALL WORK.

- Seats in a theater are curved from the front row to the back. The front row has 10 chairs, the second has 16 and the third has 22, and so on.
a) Write a recursive rule for this series:

b) Write an explicit rule for this series:

c) Using the explicit formula, find the number of chairs in row 5 (show work)

d) The auditorium can hold 17 rows of chairs. Write a sigma notation for this series, and then use either series formula to calculate how many chairs can fit in the auditorium.

Answer 1

Explanation:

sn=15+(n-1)2

the 20th row n=20 so the seats are

15+(20-1)(2)=53 seats

Explicit formula:

aₙ = a₁ + 6(n - 1) ⇒ aₙ = 10 + 6n - 6 ⇒ aₙ = 6n + 4

Write a formula to illustrate this arithmetic sequence:

Answer 2

The series:

• 10, 16, 22, ...

This is an AP with the first term a₁ = 10 and common difference d = 6

a) Recursive formula:

• a₁ = 10,
• aₙ = aₙ₋₁ + 6

b) Explicit formula:

• aₙ = a₁ + 6(n - 1) ⇒ aₙ = 10 + 6n - 6 ⇒ aₙ = 6n + 4

c) n = 5 ⇒ a₅ = ?

• a₅ = 6*5 + 4 = 34

d) S₁₇ = ?

• Sₙ = n(a₁ + aₙ)/2 = n(2a₁ + (n - 1)d)/2
• S₁₇ = 17(2*10 + 16*6)/2 = 986