Question 1202469
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The 3rd term, 36, is the first term, multiplied by the common ratio 2 times: {{{ar^2=36}}}.<br>
The 6th term, 9/2, is the first term, multiplied by the common ratio 5 times: {{{ar^5=9/2}}}.<br>
Divide the formulas for the 6th and 3rd terms to calculate the common ratio:<br>
{{{r^3=(9/2)/36=1/8}}}
{{{r=1/2}}}<br>
A RECURSIVE formula tells how to get each term from the preceding term; for a geometric sequence the rule is "multiply by the common ratio".  Since in this problem the common ratio is 1/2, the recursive formula is<br>
{{{a(n)=(1/2)*a(n-1)}}}<br>
To complete the definition of the recursive formula for the sequence, we need to specify the first term.  Since the 3rd term is 36 and the common ratio is 1/2,<br>
{{{36=a((1/2)^2)}}}
{{{36=a/4}}}
{{{a=144}}}<br>
ANSWER: a(1)=144; for n>1, a(n)=(1/2)*a(n-1)<br>