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). List the terms and successive forward differences: $$ \begin{array}{c|ccccc} \text{Terms} & 1 & 0 & ____ ___ ______ ___ _________ ____ _________ ________ __________ _____.
__________ ____ ____ _____ _____ ______ _____ _______ __________ _________ _______.
___ _________ ________ _________ ________ _____.
_______ ______ ______ ______ ___ ___ _______ ___ _____ _______ _________ _____.
______ ___ ________ _________ ______ ____ ____ ______.
_______ _____ ________ _____ ___ _______ _________ ____ ______ ____.
___ ____ ___ ___ _______ ___ ___ _______ ___ ___ _______ _____.
______ ________ ___ _____ ______ _____ _________ _________ ________ _______.
______ __________ ____ ______ ______ ___ _______.
__________ ________ ___ __________ _____ _______ _______ ______.
_________ ____ ______ __________ ______.
_____ ________ ___ ____ ______ ________ _____.
_________ __________ _________ ____ ____ ____ ______ ______ _________.
_________ _____ ___ ___ _________ ________.
_________ __________ ____ ________ ________ _________ ___ ______.
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