Final answer:
The question asks to find the average of 3^k and 3^(k+2). The average calculation leads to 5×3^k, which does not match any of the provided options, hence none of the options is correct.
Step-by-step explanation:
If k is a positive integer, which of the following represents the average of 3k and 3k+2? To determine this, we first add the two expressions and then divide by 2, since the average of two numbers is the sum of the numbers divided by 2. Here's the process:
- Add 3k and 3k+2: 3k + 3k+2 = 3k + 3k×32
- Since 32 is 9, we can rewrite the sum as: 3k + 9×3k = 3k (1 + 9) = 3k×10
- To find the average, divide the sum by 2: (3k×10) / 2 = 5×3k
However, none of the options provided (1) 3k+1 (2) 3k+2 (3) 3k+3 (4) 3k+4 represent 5×3k. Hence, none of the given options is correct.