Answer:
(a) aₙ = 22 + 6(n - 1)
(b) The 14th row has 100 seats
Explanation:
1. (a) Remember that an arithmetic series has the general formula a + (n - 1)d. Here a = the first term, and d = difference between first and second term, or in other words the difference between the nth and (n + 1)th terms.
aₙ = 22 + 6(n - 1)
This is our iterative rule for this arithmetic series, aₙ = 22 + 6(n - 1).
(b) Here n = the row number. We want to know the row number that has 100 seats. Let's equate the expression '22 + 6(n - 1)' to 100, and solve for n.
100 = 22 + 6(n - 1),
100 = 22 + 6n - 6,
100 = 16 + 6n,
6n = 84,
n = 84 / 6 = 14
=> the 14th row has 100 seats