How do you write a rule for the nth term of the geometric sequence and then find $a_{5}$ $a_5$ given $a_{4} = \frac{189}{1000}, r = \frac{3}{5}$ $a_4=189/1000, r=3/5$ ?

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How do you write a rule for the nth term of the geometric sequence and then find $a_{5}$ $a_5$ given $a_{4} = \frac{189}{1000}, r = \frac{3}{5}$ $a_4=189/1000, r=3/5$ ?

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Answer 1 · 2017-02-23T09:33:52

$a_{5} = \frac{7}{8} \times {(\frac{3}{5})}^{4} = \frac{567}{500}$ $a_5=\frac{7}{8} \times (\frac{3}{5})^4=\frac{567}{500}$

Explanation:

We know we can write every geometric sequence in the form of below:

$a_{n} = a_{1} \times r^{n - 1}$ $a_n = a_1 \times r^(n-1)$

and for now what we have to do is to figure out what is our first term ( $a_{1}$ $a_1$ ) and we can do it easily cause we have $a_{4}$ $a_4$ :

$a_{4} = \frac{189}{1000} = a_{1} \times {(\frac{3}{5})}^{3}$ $a_4=\frac{189}{1000}=a_1\times (\frac{3}{5})^3$

and we have to solve this equation for $a_{1}$ $a_1$

$a_{1} = \frac{\frac{189}{1000}}{\frac{3^{3}}{5^{3}}} = \frac{189 \times 125}{1000 \times 27} = \frac{7}{8}$ $a_1 = \frac{\frac{189}{1000}}{\frac{3^3}{5^3}} = \frac{189\times125}{1000\times27} = \frac{7}{8}$

Now we can rewrite our equation for any nth term:

$a_{n} = a_{1} \times r^{n - 1} = \frac{7}{8} \times {(\frac{3}{5})}^{n - 1}$ $a_n = a_1 \times r^(n-1) = \frac{7}{8} \times (\frac{3}{5})^(n-1)$

and we can calculate $a_{5}$ $a_5$ just by putting our $n = 5$ $n=5$ in the equation.

$a_{5} = \frac{7}{8} \times {(\frac{3}{5})}^{4} = \frac{567}{500}$ $a_5=\frac{7}{8} \times (\frac{3}{5})^4=\frac{567}{500}$

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How do you write a rule for the nth term of the geometric sequence and then find $a_{5}$ $a_5$ given $a_{4} = \frac{189}{1000}, r = \frac{3}{5}$ $a_4=189/1000, r=3/5$ ?

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How do you write a rule for the nth term of the geometric sequence and then find a_5a5a_5 given a_4=189/1000, r=3/5a4=1891000,r=35a_4=189/1000, r=3/5?

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How do you write a rule for the nth term of the geometric sequence and then find $a_{5}$ $a_5$ given $a_{4} = \frac{189}{1000}, r = \frac{3}{5}$ $a_4=189/1000, r=3/5$ ?