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Describe a pattern in the sequence of numbers. Predict the next number.
1) 1, 2, 6, 24, ___
2) 0, 3, 8, 15, 24, ___



Answer :

[tex]1)\\1=1\times1\\2=1\times2\\6=2\times3\\24=6\times4\\24\times5=120\\120\times6=720\\\vdots[/tex]

[tex]or\\1=1!\\2=2!=1\times2\\6=3!=1\times2\times3\\24=4!=1\times2\times3\times4\\5!=1\times2\times3\times4\times5=120\\6!=1\times2\times3\times4\times5\times6=720\\\vdots\\n![/tex]


[tex]2)\\0=1^2-1=1-1\\3=2^2-1=4-1\\8=3^2-1=9-1\\15=4^2-1=16-1\\24=5^2-1=25-1\\6^2-1=36-1=35\\7^2-1=49-1=48\\\vdots\\n^2-1[/tex]

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