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mollyann
Find the next three terms of the sequence. Then write a rule for the sequence. 648, 216, 72, 24
By quick observation the difference between the terms is not constant, so the sequence isn't arithmetic. It does, however, appear to be geometric:$$r=\frac{216}{648}=\frac{72}{216}=\frac{24}{72}=\frac13$$... which means we can find the next three terms by multiplying by \(\frac13\):$$\frac13(24)=8;\frac13(8)=\frac83;\frac13\left(\frac83\right)=\frac89$$The explicit form of a geometric series is \(a_n=a_1r^{n-1}\); in our case, we've identified \(r=\frac13,\ a_1=658\) which yields \(a_n=658\left(\frac13\right)^{n-1}\)