Final answer:
In an arithmetic sequence where t(6) = 33 and t(41) = 138, we can find t(0) by determining the common difference and using the formula for the nth term. The value of t(0) is -141.
Step-by-step explanation:
To find the value of t(0) in an arithmetic sequence, we need to determine the common difference between the terms. Using the given information, we can use the formula for the nth term of an arithmetic sequence t(n) = a + (n-1)d, where a is the first term and d is the common difference.
Given that t(6) = 33 and t(41) = 138, we can plug in these values to find:
t(6) = a + 5d = 33
t(41) = a + 40d = 138
Solving this system of equations, we get a = -135 and d = 6. Now we can find t(0) by substituting n = 0 into the formula:
t(0) = -135 + (0-1)(6) = -135 - 6 = -141