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

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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

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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

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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

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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

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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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