Find the 15th teum of the harmonic sequence. ½, 1, 2,please give me example and sulotion and step by step.
Answer (1)
Step-by-step explanation:Finding the 15th Term of a Harmonic SequenceUnderstanding Harmonic Sequences:A harmonic sequence is a sequence whose terms are the reciprocals of the terms of an arithmetic sequence. In simpler terms, it's a sequence where the reciprocal of each term forms an arithmetic sequence.Steps to Find the 15th Term: * Identify the corresponding arithmetic sequence: * Take the reciprocal of each term in the harmonic sequence. * In this case, the arithmetic sequence is: 2, 1, 1/2, ... * Determine the common difference: * Subtract the first term from the second term to find the common difference. * Here, the common difference (d) is 1 - 2 = -1. * Use the formula for the nth term of an arithmetic sequence: * The formula is: an = a1 + (n-1)d * Where: * an is the nth term * a1 is the first term * n is the term number * d is the common difference * Find the 15th term of the arithmetic sequence: * Using the formula: a15 = 2 + (15-1)(-1) = 2 - 14 = -12 * Take the reciprocal to find the 15th term of the harmonic sequence: * The 15th term of the harmonic sequence is 1/(-12) = -1/12.Therefore, the 15th term of the harmonic sequence 1/2, 1, 2, ... is -1/12.
