The 10th term is 87.
The 75th term is 678.
The nth term is 6 + 9(n - 1).
The given sequence is an arithmetic sequence with a common difference of 9. This means that each term is 9 more than the previous term.
To determine the appropriate term number, we can use the formula for the nth term of an arithmetic sequence:
an = a1 + d(n - 1)
where:
an is the nth term
a1 is the first term (in this case, 6)
d is the common difference (in this case, 9)
n is the term number
We can plug in the given values to solve for n:
a10 = 6 + 9 (10 - 1)
a10 = 87
Therefore, the 10th term is 87.
As for the 75th term, we can simply plug n = 75 into the formula:
a75 = 6 + 9 (75 - 1)
a75 = 678
Therefore, the 75th term is 678.
Finally, to find the nth term, we can simply substitute n into the formula:
an = 6 + 9 (n - 1)
Therefore, the nth term is 6 + 9(n - 1).