Find the indicated term of the geometric sequence algebraically.

Question

a1=18, r=4/3, 8th term

1.Find the indicated term of the geometric sequence algebraically.

Answer 1

Just to summarize what transpired in the comments:

Notice that $$a_\color{red}1=18\times\left(\frac43\right)^\color{red}0=18\times1=18$$ $$a_\color{red}2=18\times\left(\frac43\right)^\color{red}1=18\times\frac43=24$$ $$a_\color{red}3=18\times\left(\frac43\right)^\color{red}2=18\times\frac{16}9=32$$ $$\dots$$ Continuing the pattern a few more times, you'll find that $$a_\color{red}8=18\times\left(\frac43\right)^\color{red}7=18\times\frac{16384}{2187}\approx134.85$$ Problems like this become much simpler if you can find a pattern!