Final answer:
To find the first term of an arithmetic sequence, we can use the formula for the nth term. Given the 10th and 2nd terms, we set up a system of equations, solve for the common difference, then use it to find the first term. The first term is -1.
Step-by-step explanation:
To find the first term of an arithmetic sequence when given the 10th term (41/4) and the 2nd term (1/4), we can use the formula for the nth term of an arithmetic sequence: Tn = a + (n - 1)d. Here, Tn is the nth term, a is the first term, and d is the common difference.
For the 10th term (T10 = 41/4):
T10 = a + (10 - 1)d = a + 9d = 41/4
For the 2nd term (T2 = 1/4):
T2 = a + (2 - 1)d = a + d = 1/4
Now we can set up a system of equations:
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- a + 9d = 41/4
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- a + d = 1/4
Subtract the second equation from the first to find the common difference d:
(a + 9d) - (a + d) = (41/4) - (1/4)
8d = 40/4
d = 5/4
Now, insert the value of d back into the second equation:
a + (5/4) = 1/4
a = 1/4 - 5/4
a = -4/4
a = -1
The first term of the arithmetic sequence is -1.