19. `a/b` pattern series
1. Find next 3 numbers in the sequence `4/9,9/20,19/42,39/86`
I. Numerator| 4 | | 9 | | 19 | | 39 | | 79 | | `+`5 | | `+`10 | | `+`20 | | `+`40 | | | `xx`2 | | `xx`2 | | `xx`2 |
`:.` The next number for given series `4,9,19,39` is `79`
II. Denominator| 9 | | 20 | | 42 | | 86 | | 174 | | `+`11 | | `+`22 | | `+`44 | | `+`88 | | | `xx`2 | | `xx`2 | | `xx`2 |
`:.` The next number for given series `9,20,42,86` is `174`
So next numbers will be `79/174`
`:.` The next number for given series `0.4444,0.45,0.4524,0.4535` is `0.454`
Solution-1
2. Find next 3 numbers in the sequence `1/4,3/8,1/2,5/8`
Here LCM of denominator `4,8,2,8` is `8`
So number becomes `2/8,3/8,4/8,5/8`
So next numbers will be `6/8,7/8,8/8`
`:.` The next 3 number for given series `0.25,0.375,0.5,0.625` are `0.75,0.875,1`
Solution-1
3. Find next 3 numbers in the sequence `100/9,25/2,100/7,50/3`
Here LCM of numerator `100,25,100,50` is `100`
So number becomes `100/9,100/8,100/7,100/6`
So next numbers will be `100/5,100/4,100/3`
`:.` The next 3 number for given series `11.1111,12.5,14.2857,16.6667` are `20,25,33.3333`
Solution-1
4. Find next 3 numbers in the sequence `-1,1/2,-1/6,1/24,-1/120`
I. Numerator| -1 | | 1 | | -1 | | 1 | | -1 | | 1 | | `-:`-1 | | `-:`-1 | | `-:`-1 | | `-:`-1 | | `-:`-1 |
`:.` The next number for given series `-1,1,-1,1,-1` is `1`
II. Denominator| 1 | | 2 | | 6 | | 24 | | 120 | | 720 | | `xx`2 | | `xx`3 | | `xx`4 | | `xx`5 | | `xx`6 | | | `+`1 | | `+`1 | | `+`1 | | `+`1 |
`:.` The next number for given series `1,2,6,24,120` is `720`
So next numbers will be `1/720`
`:.` The next number for given series `-1,0.5,-0.1667,0.0417,-0.0083` is `0.0014`
Solution-1
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