Find the 15th teum of the harmonic sequence. ½, 1, 2,
Answer (1)
Answer:Here's how to find the 15th term of the harmonic sequence: Understanding Harmonic Sequences - A harmonic sequence is a sequence where the reciprocals of the terms form an arithmetic sequence.- In other words, if you take the reciprocal of each term in a harmonic sequence, you get a sequence where the difference between consecutive terms is constant. Steps to Find the 15th Term 1. Find the arithmetic sequence: - Take the reciprocals of the given terms: 2, 1, ½- The common difference in this arithmetic sequence is -1.2. Find the 15th term of the arithmetic sequence: - The general formula for the nth term of an arithmetic sequence is: a_n = a_1 + (n-1)d, where a_1 is the first term, d is the common difference, and n is the term number.- In this case, a_1 = 2, d = -1, and n = 15.- Therefore, the 15th term of the arithmetic sequence is: a_15 = 2 + (15 - 1)(-1) = -123. Find the reciprocal of the 15th term of the arithmetic sequence: - The 15th term of the harmonic sequence is the reciprocal of the 15th term of the arithmetic sequence.- Therefore, the 15th term of the harmonic sequence is 1/(-12) = -1/12. So, the 15th term of the harmonic sequence ½, 1, 2, ... is -1/12.
