An explicit formula for the general term for the arithmetic sequence 7/4,1, 1/4, -1/2?

-3/4

To find an explicit formula for the general term of an arithmetic sequence, you need two pieces of information: the first term (a1) and the common difference (d).

In this case, the arithmetic sequence starts with the first term (a1) of 7/4, and the common difference (d) can be calculated by subtracting any two consecutive terms. Let's subtract the second term from the first term:

1 - (7/4) = 4/4 - 7/4 = -3/4

We have found that the common difference (d) is -3/4.

Now that we have the first term (a1 = 7/4) and the common difference (d = -3/4), we can use the explicit formula for an arithmetic sequence, which is:

an = a1 + (n - 1) * d

Here, "an" represents the nth term of the sequence.

Now, let's find the general term for the arithmetic sequence you provided. We'll substitute the values into the formula:

a_n = (7/4) + (n - 1)(-3/4)

Simplifying further, we get:

a_n = 7/4 - (3/4)(n - 1)

Thus, the explicit formula for the general term of the given arithmetic sequence is:

a_n = 7/4 - (3/4)(n - 1)