Question 1157839
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#24....<br>
For any geometric sequence,
{{{a(n) = a(0)*r^(n-1)}}}<br>
The formula says exactly what the definition of a geometric sequence says: the n-th term is the first term, multiplied by the common ratio, r, (n-1) times.<br>
Note it is (n-1) times, because the first term is multiplied by the common ratio 0 times.<br>
{{{a(5)=48}}}
{{{a(4)=24}}}<br>
Formally, divide a(5) by a(4):<br>
{{{a(5)/a(4) = (a(0)r^4)/(a(0)r^3) = r}}}
{{{r = 48/24 = 2}}}<br>
Informally, simply observe that the 5th term is the 4th term multiplied by the common ratio; 48/24 = 2.<br>
We have determined r; to finish finding the explicit formula, we need to find a(0).<br>
{{{a(4) = 24 = a(0)r^3 = a(0)2^3 = 8a(0)}}}
{{{a(0) = 24/8 = 3}}}<br>
The explicit formula is
{{{a(n) = 3(2^(n-1))}}}<br>
Evaluate a(9) using the formula.<br>
Or, informally, multiply the 5th term, 48, by 2, 4 more times....<br>