Determine the nth term of a harmonic sequence.

The nth term of a harmonic sequence can be found using the formula: a_n = 1/(1/d + (n-1) * (1/a_1)), where d is the common difference and a_1 is the first term.

A harmonic sequence is a sequence of numbers where each term is the reciprocal of the corresponding term in an arithmetic sequence. For example, if the arithmetic sequence is 2, 4, 6, 8, the corresponding harmonic sequence would be 1/2, 1/4, 1/6, 1/8.

To find the nth term of a harmonic sequence, we need to know the first term and the common difference. The first term is simply the reciprocal of the first term in the corresponding arithmetic sequence. The common difference is the difference between the reciprocals of consecutive terms in the arithmetic sequence.

Using the formula a_n = 1/(1/d + (n-1) * (1/a_1)), we can plug in the values of d and a_1 to find the nth term. For example, if the first term of the harmonic sequence is 1/2 and the common difference is 1/4, we can find the 5th term as follows:

a_5 = 1/(1/4 + (5-1) * (1/2))
a_5 = 1/(1/4 + 2/2)
a_5 = 1/(1/4 + 1)
a_5 = 1/(5/4)
a_5 = 4/5

Therefore, the 5th term of the harmonic sequence is 4/5.