Answer:
The explicit rule is Ak = 1 + 2 * (k - 1)
Step-by-step explanation:
1. Let's review the information provided to us for finding the explicit rule for the sequence.
The arithmetic sequence 1, 3, 5, 7, 9, . . . represents the set of odd natural numbers.
2. Let's find the solution:
Ak = 1 + 2 * (k - 1)
For k = 1 ⇒ Ak = 1 + 2 * (1 - 1) = 1 + 2 * 0 = 1 + 0 = 1
For k = 2 ⇒ Ak = 1 + 2 * (2 - 1) = 1 + 2 * 1 = 1 + 2 = 3
For k = 3 ⇒ Ak = 1 + 2 * (3 - 1) = 1 + 2 * 2 = 1 + 4 = 5
For k = 4 ⇒ Ak = 1 + 2 * (4 - 1) = 1 + 2 * 3 = 1 + 6 = 7
For k = 5 ⇒ Ak = 1 + 2 * (5 - 1) = 1 + 2 * 4 = 1 + 8 = 9
For k = 6 ⇒ Ak = 1 + 2 * (6 - 1) = 1 + 2 * 5 = 1 + 10 = 11
For k = 7 ⇒ Ak = 1 + 2 * (7 - 1) = 1 + 2 * 6 = 1 + 12 = 13
