Final answer:
The value used for t for the 51st term of the arithmetic sequence is -971.
Step-by-step explanation:
The arithmetic sequence given is 29, 9, -11, ...
To find the value used for t for the 51st term, we notice that the common difference between the terms is -20. This is because each term is obtained by subtracting 20 from the previous term. So, we can use the formula:
tn = a + (n-1)d
where tn is the nth term, a is the first term, n is the term number, and d is the common difference.
Plugging in the values, we get:
t51 = 29 + (51-1)(-20) = 29 + 50(-20) = -971
Therefore, the value used for t for the 51st term of the arithmetic sequence is -971.