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Find the first term of the arithmetic sequence in which a₂₇=-(1)/(2) and the common difference is

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Final answer:

The first term of the arithmetic sequence is -1/2.

Step-by-step explanation:

The first term of an arithmetic sequence can be found using the formula: an = a1 + (n - 1)d, where an is the nth term, a1 is the first term, n is the position of the term, and d is the common difference.

In this case, we are given a27 = -1/2, so n = 27. We need to find a1 and the common difference. Let's plug in the values we know:

a27 = a1 + (27 - 1)d = -1/2

Simplifying this equation, we get:

a1 + 26d = -1/2

Now, we need one more equation to solve for a1 and d. We can use the fact that a1 + d = a2. Given that a27 = -1/2, we can calculate a2:

a1 + d = -1/2

Subtracting the equations, we get:

25d = 0

Therefore, the common difference, d, is 0. Now we can substitute this value back into either equation to find a1:

a1 + 26(0) = -1/2

a1 = -1/2

So, the first term of the arithmetic sequence is -1/2.

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