Question

identify a pattern in this list of numbers. then use this pattern to find the next number. (more than one pattern might exist, so it is possible that there is more than one correct answer.)
5, 15, 13, 39, 37, 111, 109, 327, ____
fill in the next number in the list.
5, 15, 13, 39, 37, 111, 109, 327, \boxed{}

Explanation:

Step1: Analyze the pattern of multiplication and subtraction

Looking at the sequence: \( 5, 15, 13, 39, 37, 111, 109, 327, \dots \)

• \( 5\times3 = 15 \)
• \( 15 - 2 = 13 \)
• \( 13\times3 = 39 \)
• \( 39 - 2 = 37 \)
• \( 37\times3 = 111 \)
• \( 111 - 2 = 109 \)
• \( 109\times3 = 327 \)

Step2: Apply the pattern to find the next number

After \( 327 \), we follow the pattern of subtracting 2 (since the pattern alternates between multiplying by 3 and subtracting by 2). So, \( 327 - 2 = 325 \)

Answer:

325