The sequence {1,2,3,5,8,13,21,...} satisfies the difference equation Xn+2=Xn+1+Xp where Xo=1 and X1=2, whose solution is shown below. Try finding the new solution if we index the sequence ahead by 1 i.e. recompute the constants starting with Xo=2 and X1=3. Try it again where Xo=3 and X1=5. Do you see a pattern? So then, what is the solution after indexing m steps ahead i.e. if the mth member in the sequence is re-indexed to be the oth member? 1+ v5 )* 1 – V5 n 5 + 3/5 5 – 3/5 Xn 10 10

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Sequence and Series

A sequence is defined as a collection of things. Series is defined to sum the things one by one in the sequence.  It was invented by German mathematician Carl Friedrich Gauss.