8. Prime numbers addition, multiplicaiton series
1. Find next 3 numbers in the sequence `6,15,35,77,143`
The series is the product of consecutive prime numbers.
`2xx3=6`
`3xx5=15`
`5xx7=35`
`7xx11=77`
`11xx13=143`
So required number are
`13xx17=221`
`17xx19=323`
`19xx23=437`
`:.` The next 3 number for given series `6,15,35,77,143` are `221,323,437`
Solution-1
2. Find next 3 numbers in the sequence `6,35,143,323,667`
The series is the product of consecutive prime numbers.
`2xx3=6`
`5xx7=35`
`11xx13=143`
`17xx19=323`
`23xx29=667`
So required number are
`31xx37=1147`
`41xx43=1763`
`47xx53=2491`
`:.` The next 3 number for given series `6,35,143,323,667` are `1147,1763,2491`
Solution-1
3. Find next 3 numbers in the sequence `5,12,24,36,52,68`
The series is the sum of consecutive prime numbers.
`2+3=5`
`5+7=12`
`11+13=24`
`17+19=36`
`23+29=52`
`31+37=68`
So required number are
`41+43=84`
`47+53=100`
`59+61=120`
`:.` The next 3 number for given series `5,12,24,36,52,68` are `84,100,120`
Solution-1
4. Find next 3 numbers in the sequence `21,55,91,187`
The series is the product of prime1*prime3 numbers.
`3xx7=21`
`5xx11=55`
`7xx13=91`
`11xx17=187`
So required number are
`13xx19=247`
`17xx23=391`
`19xx29=551`
`:.` The next 3 number for given series `21,55,91,187` are `247,391,551`
Solution-1
5. Find next 3 numbers in the sequence `1,2,6,30,210`
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1 |
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2 |
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6 |
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30 |
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210 |
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2310 |
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30030 |
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510510 |
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`xx2 ` |
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`xx3 ` |
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`xx5 ` |
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`xx7 ` |
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`xx11 ` |
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`xx13 ` |
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`xx17 ` |
`:.` The next 3 number for given series `1,2,6,30,210` are `2310,30030,510510`
Solution-1
6. Find next 3 numbers in the sequence `1,2,4,6,10,12,16,18,22,28,30,36,40`
The series is the difference of consecutive prime numbers.
`2-1=1`
`3-1=2`
`5-1=4`
`7-1=6`
`11-1=10`
`13-1=12`
`17-1=16`
`19-1=18`
`23-1=22`
`29-1=28`
`31-1=30`
`37-1=36`
`41-1=40`
So required number are
`43-1=42`
`47-1=46`
`53-1=52`
`:.` The next 3 number for given series `1,2,4,6,10,12,16,18,22,28,30,36,40` are
`42,46,52`
Solution-1
This material is intended as a summary. Use your textbook for detail explanation.
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