4. Square, Cube, Power series
1. Find next 3 numbers in the sequence `1,4,9,16,25`
Series are based on square of a number `1=1^2,4=2^2,9=3^2,16=4^2,25=5^2`
`:.` The next 3 number for given series `1,2,3,4,5` are `6,7,8`
`:.` Next possible number are `6^2=36,7^2=49,8^2=64`
`:.` The next 3 number for given series `1,4,9,16,25` are `36,49,64`
Solution-1
2. Find next 3 numbers in the sequence `1,8,27,64,125`
Series are based on cube of a number `1=1^3,8=2^3,27=3^3,64=4^3,125=5^3`
`:.` The next 3 number for given series `1,2,3,4,5` are `6,7,8`
`:.` Next possible number are `6^3=216,7^3=343,8^3=512`
`:.` The next 3 number for given series `1,8,27,64,125` are `216,343,512`
Solution-1
3. Find next 3 numbers in the sequence `5,25,26,676`
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5 |
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25 |
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26 |
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676 |
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677 |
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458329 |
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458330 |
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`^`2 |
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`+`1 |
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`^`2 |
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`+`1 |
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`^`2 |
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`+`1 |
`:.` The next 3 number for given series `5,25,26,676` are `677,458329,458330`
Solution-1
4. Find next 3 numbers in the sequence `676,26,25,5`
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676 |
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26 |
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25 |
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5 |
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4 |
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2 |
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1 |
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`^`1/2 |
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`-`1 |
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`^`1/2 |
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`-`1 |
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`^`1/2 |
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`-`1 |
`:.` The next 3 number for given series `676,26,25,5` are `4,2,1`
Solution-1
5. Find next 3 numbers in the sequence `7,26,63,124,215`
`2^3-1=7`
`3^3-1=26`
`4^3-1=63`
`5^3-1=124`
`6^3-1=215`
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2 |
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3 |
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4 |
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5 |
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6 |
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7 |
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8 |
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9 |
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`+`1 |
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`+`1 |
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`+`1 |
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`+`1 |
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`+`1 |
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`+`1 |
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`+`1 |
`:.` The next 3 number for given series `2,3,4,5,6` are `7,8,9`
`7^3-1=342`
`8^3-1=511`
`9^3-1=728`
`:.` The next 3 number for given series `7,26,63,124,215` are `342,511,728`
Solution-1
6. Find next 3 numbers in the sequence `7,23,47,119,167`
`3^2-2=7`
`5^2-2=23`
`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 `3,5,7,11,13` are `17,19,23`
`17^2-2=287`
`19^2-2=359`
`23^2-2=527`
`:.` The next 3 number for given series `7,23,47,119,167` are `287,359,527`
Solution-1
7. Find next 3 numbers in the sequence `1,4,27,256,3125`
`1^1=1`
`2^2=4`
`3^3=27`
`4^4=256`
`5^5=3125`
So required number are
`6^6=46656`
`7^7=823543`
`8^8=16777216`
Answer : `46656,823543,16777216`
`:.` The next 3 number for given series `1,4,27,256,3125` are `46656,823543,16777216`
Solution-1
8. Find next 3 numbers in the sequence `0,7,26,63,124`
`1^3-1=0`
`2^3-1=7`
`3^3-1=26`
`4^3-1=63`
`5^3-1=124`
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1 |
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2 |
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3 |
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4 |
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5 |
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6 |
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7 |
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8 |
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`+`1 |
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`+`1 |
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`+`1 |
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`+`1 |
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`+`1 |
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`+`1 |
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`+`1 |
`:.` The next 3 number for given series `1,2,3,4,5` are `6,7,8`
`6^3-1=215`
`7^3-1=342`
`8^3-1=511`
`:.` The next 3 number for given series `0,7,26,63,124` are `215,342,511`
Solution-1
This material is intended as a summary. Use your textbook for detail explanation.
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