15. `x^2,x^3` alternate type series
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
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
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
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
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
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
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
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
This material is intended as a summary. Use your textbook for detail explanation.
Any bug, improvement, feedback then
|
