SOLUTION: Find the nth term of the harmonic sequence 4/5,2/3,4/7,... n=12

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Question 1165029: Find the nth term of the harmonic sequence
4/5,2/3,4/7,... n=12
Answer by Edwin McCravy(20056) About Me  (Show Source):
You can put this solution on YOUR website!
4/5,2/3,4/7,... n=12

First we get the nth term of the reciprocals, 

5/4,3/2,7/4,...

which is an arithmetic sequence with first term 5/4 and common difference
3/2-5/4 = 6/4-5/4 = 1/4
7/4-3/2 = 7/4-6/4 = 1/4

an = a1+(n-1)d

a%5Bn%5D=5%2F4%2B%28n-1%29expr%281%2F4%29

a%5Bn%5D=5%2F4%2Bn%2Aexpr%281%2F4%29-1%2Aexpr%281%2F4%29

a%5Bn%5D=5%2F4%2Bn%2Aexpr%281%2F4%29-1%2F4

a%5Bn%5D=4%2F4%2Bexpr%281%2F4%29n

a%5Bn%5D=%284%2Bn%29%2F4

So when n=12

a%5Bn%5D=%284%2B12%29%2F4

a%5Bn%5D=%2816%29%2F4

a%5Bn%5D=4

So the 12th term of the given harmonic sequence is the reciprocal of 4.

Answer:  1/4

-----------------------------

Checking with a TI-84

Type in 4/5 
press MATH ENTER ENTER

Type in 

(,  2ND, (-), x-1, +, 1, /, 4, ), x-1, MATH, ENTER   
 
note: the (-) refers to the 'negative' key at the bottom just below the 3.  

Then press ENTER over and over to generate the terms up to the 12th one:

  1   2   3   4   5   6    7   8    9  10   11  12 
4/5,2/3,4/7,1/2,4/9,2/5,4/11,1/3,4/13,2/7,4/15,1/4 

Edwin