Given the arithmetic sequence 32,12,−12,−32, . . .%0D%0A3%0D%0A2%0D%0A,%0D%0A1%0D%0A2%0D%0A,%0D%0A−%0D%0A1%0D%0A2%0D%0A,%0D%0A−%0D%0A3%0D%0A2%0D%0A,%0D%0A %0D%0A.%0D%0A %0D%0A.%0D%0A %0D%0A.%0D%0A, find the common difference.(1 point)%0D%0AThe common difference of the arithmetic sequence is d=%0D%0A%0D%0A=%0D%0A.
The common difference d can be calculated by taking the difference between any two consecutive terms in the arithmetic sequence.
For example, taking the difference between the first two terms 32 and 12:
d = 12 - 32 = -20
Similarly, taking the difference between the next two terms 12 and -12:
d = -12 - 12 = -24
Taking the difference between the next two terms -12 and -32:
d = -32 - (-12) = -20
Since the common difference should remain constant in an arithmetic sequence, we can see that the common difference is -20.
This is wrong
Apologies for the mistake. Let's try to calculate the correct common difference for the arithmetic sequence.
To find the common difference (d) in an arithmetic sequence, we identify two consecutive terms and subtract the first term from the second term.
For the given arithmetic sequence:
32, 12, -12, -32, ...
Let's calculate the common difference using the first two terms:
d = 12 - 32
d = -20
Now, let's verify this common difference by calculating the difference between the rest of the consecutive terms:
12 - (-12) = 24
-12 - (-32) = 20
It seems that the common difference indeed changes with each step in the sequence, making it a non-constant difference sequence rather than a true arithmetic sequence. Apologies for the confusion earlier.