Final answer:
To find the common difference of an arithmetic sequence when the 100th term is known, one must know the value of at least one other term in the sequence, ideally the first term.
Step-by-step explanation:
If the 100th term of an arithmetic sequence is known, to find the common difference you would need additional information about another term in the sequence.
Typically, knowing the first term (a1) alongside the formula for the nth term of an arithmetic sequence, which is an = a1 + (n-1)d where d is the common difference, would allow you to solve for d.
In this case, since we have the 100th term, we can use the formula a100 = a1 + (100-1)d. By substituting the value of the 100th term into this equation and knowing the value of the first term a1, we can then rearrange to solve for the common difference.
To find the common difference in an arithmetic sequence, we need to know the value of the 100th term and at least one other term in the sequence. This is because the common difference is the difference between consecutive terms in the sequence. By knowing the 100th term and another term, we can subtract the two terms to find the common difference.