Question 914116: 3,6/7,9/17,12/31,15/49,18/71 is my sequence what are the next 2 numbers in the sequence
Answer by KMST(5328)   (Show Source):
You can put this solution on YOUR website! 21/97 and 24/127
Numerators increase by 3
3 6 9 12 15 18 21 24 ...
The difference from one denominator to the next changes.
It starts with 6 and increases by 4 each time.
The first number is 3/1; the denominator is 1.
The second denominator is 6 more:
1+6=7,
and the second number is 6/7.
The third denominator is
6+4=10 more than the second:
7+10=17.
So the third number is 9/17.
To get the next denominator, you have to add 10+4=14, to get 17+14=31.
With that denominator, you get 12/31.
Next, you add 14+4=18 to get 31+18=49, for 15/49.
Then, you add 18+4=22 to get 49+22=71, for 18/71.
Then you add 22+4=26 to get 71+26=97, for 21/97.
Then you add 26+4=30 to get 97+30=127 for 24/127.
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