Harmonic Sequence

 

Harmonic sequence – is a sequence such that the reciprocals of the terms form an arithmetic sequence. EXAMPLE ½, ¼, 1/6, 1/8

 

Fibonacci sequence – is a sequence where its first two terms are either both 1, or 0 and 1; and each term, thereafter, is obtained by

 

adding the two preceding terms. EXAMPLE 0, 1, 1,2, 3, 5, … 

 

State whether the given sequence is arithmetic, geometric, harmonic, or part of a Fibonacci. Then, give the next term of the sequence. 1. 8, 8, 16, 24, 32, … 

 

2. 1/3, 1/3, 1/9, 1/27, 1/81,…  3. 1296, 1296, 216, 36, 6, …  4. 8, 13,21, 3 34, 55, …  5. ¾, ¾, 1, , , …      4       6.  , , , , …  4 0 6 

 

 2√ 2 5√ 2 8√ 2 11√ 2, … 7. 6   ,6   6 ,   6 ,   8.  , , , , …   7 3 9

9. 6, -18, 54, -162,…    

10. 40, 8,  ,  , … 

 

Find the indicated term of the following harmonic sequence. 0 0 0 th 1. 3   , 6   , 9   , … 6  term      th

 

2. 4 ,  , 4 ,   term  , …13 th 3.  , , , , …15  term  3 7 

 

th

Find the 8  term of the harmonic sequence.    1.  ,  , 3 , …     

 

th

2. 3 , 7 ,  , …10  term th 3. 2, 2, , , , …8  term  9 