What Is The Nth Term Of The Harmonic Sequence1/2, 1/4, 1/6, 1/8,...?, A. 1/N+1, B. 1/N^2+1, C. 1/2n, D. 1/4n-2

What is the nth term of the harmonic sequence1/2, 1/4, 1/6, 1/8,...? a. 1/n+1
b. 1/n^2+1
c. 1/2n
d. 1/4n-2

 

Harmonic Sequence

Finding the nth Term

 The nth term of the harmonic sequence 1/2, 1/4, 1/6, 1/8,...is 1/2n.

Solution:

  1. Take the corresponding arithmetic sequence of the given harmonic sequence by the reciprocals. Thus, Arithmetic Sequence: 2, 4, 6, 8
  2. Given such reciprocals, find the common difference using any two consecutive terms of the sequence. For instance, the second and the first term such that, d = 4 - 2 thus, d = 2.
  3. Using d = 2, find the nth term of the sequence by multiplying d with n where n is the last term such that dn = 2n.
  4. To complete the harmonic sequence, get the reciprocal of 2n which is 1/2n.
  5. Therefore, the nth term of the harmonic sequence 1/2, 1/4, 1/6, 1/8,… will be 1/2n.

Definition:

       Harmonic sequence is a set of numbers formed by taking the reciprocals of the succeeding terms of an arithmetic sequence.

Code: 10.3.1.1

For more details regarding harmonic means and sequence, go to the following links:

brainly.ph/question/179051

brainly.ph/question/224652

brainly.ph/question/825249


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