Question

Find the common difference of the sequence shown: ( 1/2}, 1/4}, 0, ... )

a) -(1/2)

b) -(1/8)

c) -(1/4)

Answer 1

The common difference of the sequence is found by subtracting subsequent terms, which yields a negative value indicating a decrease in the sequence. The correct common difference for the given sequence (1/2, 1/4, 0, ...) is -1/4.

Step-by-step explanation:

To find the common difference of the sequence (1/2, 1/4, 0, ...), we need to subtract each term from the subsequent term. If we subtract the second term (1/4) from the first term (1/2), we get:

1/2 - 1/4 = 2/4 - 1/4 = 1/4

Next, subtract the third term (0) from the second term (1/4):

1/4 - 0 = 1/4

However, we must recognize that we are moving from a positive value to a value of zero, which means the sequence is decreasing. Therefore, the common difference should also reflect this decrease. The actual common difference would be negative, as we are subtracting a larger number from a smaller number as we move from left to right in the sequence. Hence, the correct answer is:

c) -(1/4)