Question

If the reclusive rule for a geometric sequence is a1 = 6 an = 2an-1.

What would be the explicit rule?

Answer 1

`\text{The explicit rule of geometric sequence}\\\\a_n=a_1 r^(n-1)\\------------------------------\\\text{We have the recursive form}\ a_1=6,\ a_n=2\cdot a_(n-1).\\\\\text{Therefore}\ r=2.\ \text{Substitute:}\\\\a_n=6\cdot2^(n-1)=6\cdot2^n\cdot2^(-1)=6\cdot2^n\cdot(1)/(2)=\boxed{3\cdot2^n}`