12. Each number digits are `a^2b^2` format
1. Find next 3 numbers in the sequence `01,14,49,916,1625,2536`
`01=(0^2)(1^2)=(0)(1)=01`
`14=(1^2)(2^2)=(1)(4)=14`
`49=(2^2)(3^2)=(4)(9)=49`
`916=(3^2)(4^2)=(9)(16)=916`
`1625=(4^2)(5^2)=(16)(25)=1625`
`2536=(5^2)(6^2)=(25)(36)=2536`
So required number are
`3649=(6^2)(7^2)=(36)(49)=3649`
`4964=(7^2)(8^2)=(49)(64)=4964`
`6481=(8^2)(9^2)=(64)(81)=6481`
`:.` The next 3 number for given series `1,14,49,916,1625,2536` are `3649,4964,6481`
Solution-1
2. Find next 3 numbers in the sequence `10,41,94,169,2516,3625`
`10=(1^2)(0^2)=(1)(0)=10`
`41=(2^2)(1^2)=(4)(1)=41`
`94=(3^2)(2^2)=(9)(4)=94`
`169=(4^2)(3^2)=(16)(9)=169`
`2516=(5^2)(4^2)=(25)(16)=2516`
`3625=(6^2)(5^2)=(36)(25)=3625`
So required number are
`4936=(7^2)(6^2)=(49)(36)=4936`
`6449=(8^2)(7^2)=(64)(49)=6449`
`8164=(9^2)(8^2)=(81)(64)=8164`
`:.` The next 3 number for given series `10,41,94,169,2516,3625` are `4936,6449,8164`
Solution-1
3. Find next 3 numbers in the sequence `49,1625,3649`
`49=(2^2)(3^2)=(4)(9)=49`
`1625=(4^2)(5^2)=(16)(25)=1625`
`3649=(6^2)(7^2)=(36)(49)=3649`
So required number are
`6481=(8^2)(9^2)=(64)(81)=6481`
`100121=(10^2)(11^2)=(100)(121)=100121`
`144169=(12^2)(13^2)=(144)(169)=144169`
`:.` The next 3 number for given series `49,1625,3649` are `6481,100121,144169`
Solution-1
4. Find next 3 numbers in the sequence `49,925,2549,49121`
`49=(2^2)(3^2)=(4)(9)=49`
`925=(3^2)(5^2)=(9)(25)=925`
`2549=(5^2)(7^2)=(25)(49)=2549`
`49121=(7^2)(11^2)=(49)(121)=49121`
So required number are
`121169=(11^2)(13^2)=(121)(169)=121169`
`169289=(13^2)(17^2)=(169)(289)=169289`
`289361=(17^2)(19^2)=(289)(361)=289361`
`:.` The next 3 number for given series `49,925,2549,49121` are `121169,169289,289361`
Solution-1
5. Find next 3 numbers in the sequence `11,24,39,416,525`
`11=(1)(1^2)=(1)(1)=11`
`24=(2)(2^2)=(2)(4)=24`
`39=(3)(3^2)=(3)(9)=39`
`416=(4)(4^2)=(4)(16)=416`
`525=(5)(5^2)=(5)(25)=525`
So required number are
`636=(6)(6^2)=(6)(36)=636`
`749=(7)(7^2)=(7)(49)=749`
`864=(8)(8^2)=(8)(64)=864`
`:.` The next 3 number for given series `11,24,39,416,525` are `636,749,864`
Solution-1
6. Find next 3 numbers in the sequence `11,48,927,1664,25125`
`11=(1^2)(1^3)=(1)(1)=11`
`48=(2^2)(2^3)=(4)(8)=48`
`927=(3^2)(3^3)=(9)(27)=927`
`1664=(4^2)(4^3)=(16)(64)=1664`
`25125=(5^2)(5^3)=(25)(125)=25125`
So required number are
`36216=(6^2)(6^3)=(36)(216)=36216`
`49343=(7^2)(7^3)=(49)(343)=49343`
`64512=(8^2)(8^3)=(64)(512)=64512`
`:.` The next 3 number for given series `11,48,927,1664,25125` are `36216,49343,64512`
Solution-1
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