Word Count : 172

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We are given the sequence from the second term onward: $a_2=1,\;a_3=0,\;a_4=3,\;a_5=8,\;a_6=-1$. Use a difference table and assume the highest displayed difference becomes constant (so we can extend backwards). ____ ________ ______ ________ _______ _____ ______ _____ ___ _______.
_________ ______ ___ ________ _________ ____ ________ ______.
_______ ____ ____ __________ _________.
________ _____ ________ ______ ________ ___.
________ _____ ___ _____ __________ ______ ______ ___ __________ ________ _______.
____ __________ _________ ______ __________ ______ ________ ____ _______.
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_______ ________ _________ __________ ____ _______ ____ ______ ______ ______.
_______ _________ __________ ___ ________ ___ _______ _________ __________ ________ _______ _____.
_______ ______ ________ _____ __________ ____ _______ _______ _______ ___ _____.
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_________ ________ ____ __________ _________ __________ _______ _____ ________ ______ __________ ________.
___ ________ _____ ___ ______ __________ ______ __________ _______ _________ _______ ____.
_______ _____ ______ ____ _____ _______ ____ ______ ________ ___.
_____ _______ _________ ___ ___ ______ ________ ______ ___.
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