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find the 9th term for 3/2,1/2,3/10,3/14

Sagot :

Shyrelleshanemidn

Answer:

Find the 9th term of the harmonic sequence

3%2F2,1%2F2,3%2F10,3%2F14,... n=9

Get their reciprocals:

Step-by-step explanation:

Find the 9th term of the harmonic sequence

3%2F2,1%2F2,3%2F10,3%2F14,... n=9

Get their reciprocals:

2/3,2/1,10/3,14/3,... n=9

If we write the 2%2F1 with a 3 denominator, as 6/3

we can see the arithmetic sequence which the reciprocals form:

2/3,6/3,10/3,14/3,... n=9

Extend it to 9 terms by adding common ratio 4/3 each time:

2/3,6/3,10/3,14/3,18/3,2/3,2/3,30/3,34/3

Reduce all the fraction that will reduce:

2/3,2/1,10/3,14/3,6/1,22/3,2/3,10/1,34/3

Take the reciprocals:

3/2,1/2,3/10,3/14,1/6,3/22,3/26,1/10,3/34

9th term is 3/34

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