# Write a rule for the nth term of the geometric sequence and then find a_5 given a_4=189/1000,r=3/5

Write a rule for the nth term of the geometric sequence and then find ${a}_{5}$ given ${a}_{4}=\frac{189}{1000},r=\frac{3}{5}$
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Mario Monroe
We know we can write every geometric sequence in the form of below:
${a}_{n}={a}_{1}×{r}^{n-1}$
and for now what we have to do is to figure out what is our first term ( ${a}_{1}$ ) and we can do it easily cause we have ${a}_{4}$:
${a}_{4}=\frac{189}{1000}={a}_{1}×{\left(\frac{3}{5}\right)}^{3}$
and we have to solve this equation for ${a}_{1}$
${a}_{1}=\frac{\frac{189}{1000}}{\frac{{3}^{3}}{{5}^{3}}}=\frac{189×125}{1000×27}=\frac{7}{8}$
Now we can rewrite our equation for any nth term:
${a}_{n}={a}_{1}×{r}^{n-1}=\frac{7}{8}×{\left(\frac{3}{5}\right)}^{n-1}$
and we can calculate ${a}_{5}$ just by putting our n=5 in the equation.
${a}_{5}=\frac{7}{8}×{\left(\frac{3}{5}\right)}^{4}=\frac{567}{500}$