Question

use inductive reasoning to find a pattern, and then make a reasonable conjecture for the next nu 1 5 3 7 5 9 7 11

Explanation:

Step1: Split into two sub-patterns

Separate the sequence into odd-positioned and even-positioned terms:
Odd positions (1st, 3rd, 5th, 7th): $1, 3, 5, 7$
Even positions (2nd, 4th, 6th, 8th): $5, 7, 9, 11$

Step2: Identify sub-pattern rules

For odd positions: each term increases by 2.
For even positions: each term increases by 2.

Step3: Find the next term

The missing term is the 9th position (odd), so take the 7th term ($7$) and add 2.
$7 + 2 = 9$

Answer:

$9$