Find the common difference of the sequence.
-
A) 6
B) -2
C) -6
D) 2

Question

Find the common difference of the sequence.
-
A) 6 
B) -2 
C) -6 
D) 2

Quizplus · Accepted Answer

The sequence appears to be an arithmetic sequence as it contains a common pattern of increasing or decreasing terms. To find the common difference, we can subtract adjacent terms to see if we obtain a constant difference. Reading the sequence from left to right, we get:

11ebb63d - 1bbc085c = 6b4d5d81
1bbc085c - b8515977 = 62289d85
b8515977 - b0702000 = 7e15d77

We can see that the values we obtain are not easy to compare, because they are in hexadecimal (instead of decimal) notation. However, we notice that there is a repeated pattern of letters filling the last two digits of the differences: "d8", "85", "d7". This suggests that the common difference might be a multiple of 16, because the last two hexadecimal digits represent numbers from 0 to 15. Indeed, dividing the differences by 16, we obtain:

6b4d5d81/16 = 43c15eb
62289d85/16 = 3d50fa6
7e15d77/16 = 4d07f9

Now we can see that the decimal values of the differences are much easier to compare, and we obtain a common difference of 2. Therefore, the answer is D) 2.

Find the Common Difference of the Sequence