Answered

IDNLearn.com is designed to help you find the answers you need quickly and easily. Our community is here to provide detailed and trustworthy answers to any questions you may have.

3. What is the common difference of the arithmetic progression (AP) [tex]$x-1, x-2, x-3, x-4, \ldots$[/tex]?

A. 1
B. 0
C. -1
D. 2

Sagot :

GinnyAnsweridn
To determine the common difference in an arithmetic progression (AP), we need to look at the difference between successive terms. The common difference [tex]\(d\)[/tex] is defined as the difference between any two consecutive terms in the sequence.

Consider the given AP: [tex]\(x-1, x-2, x-3, x-4, \ldots\)[/tex].

To find the common difference, we subtract the second term from the first term:
- First term: [tex]\(x-1\)[/tex]
- Second term: [tex]\(x-2\)[/tex]

The common difference [tex]\(d\)[/tex] is:
[tex]\[ d = (x-2) - (x-1) \][/tex]

Now, let's simplify the expression:
[tex]\[ d = x - 2 - (x - 1) \][/tex]

[tex]\[ d = x - 2 - x + 1 \][/tex]

[tex]\[ d = x - x - 2 + 1 \][/tex]

[tex]\[ d = -1 \][/tex]

Therefore, the common difference [tex]\(d\)[/tex] of the arithmetic progression [tex]\(x-1, x-2, x-3, x-4, \ldots\)[/tex] is [tex]\(-1\)[/tex].

So, the correct answer is:
c) -1
We are delighted to have you as part of our community. Keep asking, answering, and sharing your insights. Together, we can create a valuable knowledge resource. Find clear and concise answers at IDNLearn.com. Thanks for stopping by, and come back for more dependable solutions.