What is the nth term when the Sequence is
0 first term
0 second term
420 sixty-ninth term
Since the common difference is 0, all the terms are the same as the first term: 0
To find the nth term of a sequence, we need to identify the pattern in the given sequence. Looking at the given sequence:
0 (first term)
0 (second term)
420 (sixty-ninth term)
From the given sequence, it is not immediately clear what the pattern is. However, we can look for a relationship between terms to find a pattern.
Let's examine the difference between consecutive terms:
0 (second term) - 0 (first term) = 0
420 (sixty-ninth term) - 0 (second term) = 420
We can observe that the difference between consecutive terms is constant. Therefore, the sequence follows an arithmetic pattern.
To find the nth term of this arithmetic sequence, we need to determine the common difference. In this case, the common difference is 420 - 0 = 420.
Using the formula for the nth term of an arithmetic sequence:
nth term = first term + (n - 1) * common difference
Where:
- first term is the initial term of the sequence (0 in this case)
- n is the position of the desired term
- common difference is the difference between consecutive terms (420 in this case)
Applying the formula, we get:
nth term = 0 + (n - 1) * 420
Therefore, the formula for the nth term of this sequence is:
nth term = 420n - 420