7. Prime numbers series
1. Find next 3 numbers in the sequence `2,3,5,7`
The given numbers are prime numbers and next 3 prime number are 11,13,17
`:.` The next 3 number for given series `2,3,5,7` are `11,13,17`
Solution-1
2. Find next 3 numbers in the sequence `2,5,11,17`
The given numbers are prime numbers and next 3 prime number are 23,31,41
`:.` The next 3 number for given series `2,5,11,17` are `23,31,41`
Solution-1
3. Find next 3 numbers in the sequence `4,9,25,49`
Series are based on square of a number `4=2^2,9=3^2,25=5^2,49=7^2`
`:.` The next 3 number for given series `2,3,5,7` are `11,13,17`
`:.` Next possible number are `11^2=121,13^2=169,17^2=289`
`:.` The next 3 number for given series `4,9,25,49` are `121,169,289`
Solution-1
4. Find next 3 numbers in the sequence `-2,-3,-5,-7,-11`
Here given series is -ve series. So we consider it only +ve series
New series is : `2,3,5,7,11`
The given numbers are prime numbers and next 3 prime number are 13,17,19
Now again adding -ve to all, we get
Answer : `-13,-17,-19`
`:.` The next 3 number for given series `-2,-3,-5,-7,-11` are `-13,-17,-19`
Solution-1
5. Find next 3 numbers in the sequence `47,119,167`
`7^2-2=47`
`11^2-2=119`
`13^2-2=167`
The given numbers are prime numbers and next 3 prime number are 17,19,23
`:.` The next 3 number for given series `7,11,13` are `17,19,23`
`17^2-2=287`
`19^2-2=359`
`23^2-2=527`
`:.` The next 3 number for given series `47,119,167` are `287,359,527`
Solution-1
6. Find next 3 numbers in the sequence `6,12,30,56,132`
`2^2+2=6`
`3^2+3=12`
`5^2+5=30`
`7^2+7=56`
`11^2+11=132`
The given numbers are prime numbers and next 3 prime number are 13,17,19
`:.` The next 3 number for given series `2,3,5,7,11` are `13,17,19`
`13^2+13=182`
`17^2+17=306`
`19^2+19=380`
`:.` The next 3 number for given series `6,12,30,56,132` are `182,306,380`
Solution-1
This material is intended as a summary. Use your textbook for detail explanation.
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