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

1 Answer
Feb 23, 2017

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)

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\times (\frac{3}{5})^3

and we have to solve this equation for a_1

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)

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

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