Question

A recursive rule for a geometric sequence is a1=3;an=1/2an−1.

What is the explicit rule for this sequence?



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Answer 1

`\text{The explicit rule of geometric sequence}\\\\a_n=a_1 r^(n-1)\\------------------------------\\\text{We have the recursive form}\ a_1=3,\ a_n=(1)/(2)\cdot a_(n-1).\\\\\text{Therefore}\ r=(1)/(2).\ \text{Substitute:}\\\\\boxed{a_n=3\left((1)/(2)\right)^(n-1)}`