second term= mixed fraction 6 1/2 and Tenth term= mixed fraction 18 1/2, determine the nth term and the first term and
To find the nth term, we need to determine the common difference between each term.
From the second term to the tenth term, there are 10 - 2 = 8 terms in between.
The difference between the second term (6 1/2) and the tenth term (18 1/2) is 18 1/2 - 6 1/2 = 12.
Therefore, the common difference is 12/8 = 3/2.
To find the first term, subtract the common difference (3/2) from the second term (6 1/2):
6 1/2 - 3/2 = 6 - 3/2 = 5 1/2.
So, the first term is 5 1/2.
The nth term can be found using the formula:
nth term = first term + (n - 1) * common difference.
Substituting the values we found, we have:
nth term = (5 1/2) + (n - 1) * (3/2)
This is the formula for finding the nth term of the given sequence.