Directions: Find the next fie terms, then wrike a conjecture. 1. \( 13,18,23,28,33 \) conjecture: 2. \( 512,255,128,64 \) conjecture:

To find the next five terms and write a conjecture for each sequence, we need to identify the pattern in each sequence. 1. For the sequence \( 13, 18, 23, 28, 33 \): The difference between consecutive terms is: \( 18 - 13 = 5 \) \( 23 - 18 = 5 \) \( 28 - 23 = 5 \) \( 33 - 28 = 5 \) Since the difference is constant (5), the sequence is arithmetic, and each term is 5 more than the previous term. To find the next five terms: \( 33 + 5 = 38 \) \( 38 + 5 = 43 \) \( 43 + 5 = 48 \) \( 48 + 5 = 53 \) \( 53 + 5 = 58 \) Conjecture: The next five terms of the sequence are 38, 43, 48, 53, and 58. The sequence is an arithmetic sequence with a common difference of 5. 2. For the sequence \( 512, 255, 128, 64 \): The difference between consecutive terms is: \( 255 - 512 = -257 \) \( 128 - 255 = -127 \) \( 64 - 128 = -64 \) The differences are not constant, so the sequence is not arithmetic. However, the differences are multiples of 127 (since -257 is -1 * 127, -127 is -1 * 127, and -64 is -1 * 127). This suggests that the sequence might be geometric, where each term is a multiple of 127 of the previous term. To find the next five terms, we can divide each term by 2 (since the sequence seems to be decreasing by half each time): \( 64 / 2 = 32 \) \( 32 / 2 = 16 \) \( 16 / 2 = 8 \) \( 8 / 2 = 4 \) \( 4 / 2 = 2 \) Conjecture: The next five terms of the sequence are 32, 16, 8, 4, and 2. The sequence is a geometric sequence with a common ratio of 1/2.