Final answer:
The missing coefficient in the sequence _ 4 8 10 22 is determined by finding the constant multiplier for the base ratio 2:1:2, which is 2.
Step-by-step explanation:
The student is asking to find the missing coefficient in a given sequence. The sequence provided is: _ 4 8 10 22. To determine the pattern, we should look at the relationships between the numbers. Since the significant clue provided is that the ratio of 22:11:22 reduces to 2:1:2, it suggests that the sequence is based on multiplying a constant to these basic ratios. Therefore, if we consider the sequence 2:1:2 as the simplified form, then multiplying each term by the same number should give us the sequence in the question. Knowing the second number is 4, the pattern seems to be multiplied by 2 (since 2 x 2 = 4). To confirm, we multiply the third ratio number by 2 as well (2 x 2 = 4), matching the next number in the sequence, which is 8. Lastly, 2 x 11 gives us 22, which is the last number in the sequenced provided.