1. Find next 3 numbers in the sequence `1,8,9,64,25`

`1^2=1`

`2^3=8`

`3^2=9`

`4^3=64`

`5^2=25`

So required number are
`6^3=216`

`7^2=49`

`8^3=512`

`:.` The next 3 number for given series `1,8,9,64,25` are `216,49,512`

Solution-1

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2. Find next 3 numbers in the sequence `7,8,63,24`

`2^3-1=7`

`3^2-1=8`

`4^3-1=63`

`5^2-1=24`

So required number are
`6^3-1=215`

`7^2-1=48`

`8^3-1=511`

`:.` The next 3 number for given series `7,8,63,24` are `215,48,511`

Solution-1

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3. Find next 3 numbers in the sequence `1,4,27,16,125`

`1^3=1`

`2^2=4`

`3^3=27`

`4^2=16`

`5^3=125`

So required number are
`6^2=36`

`7^3=343`

`8^2=64`

`:.` The next 3 number for given series `1,4,27,16,125` are `36,343,64`

Solution-1

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4. Find next 3 numbers in the sequence `1,32,243,1024`

Series are based on cube of a number `1=1^5,32=2^5,243=3^5,1024=4^5`

`:.` The next 3 number for given series `1,2,3,4` are `5,6,7`

`:.` Next possible number are `5^5=3125,6^5=7776,7^5=16807`

`:.` The next 3 number for given series `1,32,243,1024` are `3125,7776,16807`

Solution-1

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5. Find next 3 numbers in the sequence `0,1,16,81,256`

Series are based on cube of a number `0=0^4,1=1^4,16=2^4,81=3^4,256=4^4`

`:.` The next 3 number for given series `0,1,2,3,4` are `5,6,7`

`:.` Next possible number are `5^4=625,6^4=1296,7^4=2401`

`:.` The next 3 number for given series `0,1,16,81,256` are `625,1296,2401`

Solution-1

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6. Find next 3 numbers in the sequence `64,243,256,125,36`

`2^6=64`

`3^5=243`

`4^4=256`

`5^3=125`

`6^2=36`

So required number are
`7^1=7`

`8^0=1`

`9^-1=0.1111`

Answer : `7,1,0.1111`

`:.` The next 3 number for given series `64,243,256,125,36` are `7,1,0.1111`

Solution-1

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7. Find next 3 numbers in the sequence `49,216,625,1024,729`

`7^2=49`

`6^3=216`

`5^4=625`

`4^5=1024`

`3^6=729`

So required number are
`2^7=128`

`1^8=1`

`0^9=0`

Answer : `128,1,0`

`:.` The next 3 number for given series `49,216,625,1024,729` are `128,1,0`

Solution-1

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8. Find next 3 numbers in the sequence `1,32,81,64,25`

`1^6=1`

`2^5=32`

`3^4=81`

`4^3=64`

`5^2=25`

So required number are
`6^1=6`

`7^0=1`

`8^-1=0.125`

Answer : `6,1,0.125`

`:.` The next 3 number for given series `1,32,81,64,25` are `6,1,0.125`

Solution-1

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