Question

Help with geometric sequence please! Find the nth term for the following geometric sequence:
t4 = 8x^3 and t9 = 5x^20

Answer 1

\[t9=8x^{3} and t9 = 5x^{20}\]

Answer 2

this is what I have:
t4 = 8x^3
8x^3 = ar^3
a = 8x^3 / r^3
5x^20 = ar^19
5x^20 = (8x^3)(r^19) / r^3
5x^20 = (8x^3)(r^16)
5x^20 / 8x^3 = (8x^3)(r^3) / 8x^3
0.625x^17 = r^16

Now I'm stuck.

Answer 3

In the problem, is t_{9} or t_{19}?

Answer 4

t9 = term 9. the answer is supposed to e tn = (2x)^n-1 but I don't know how to get it

Answer 5

Then, I thin it should be this way,
\[t_n=t_1r^{n-1}\]\[t_4=t_1r^3=8x^3\\
t_9=t_1r^8=5x^{20}\] Divide both expressions, to find r,
\[\frac{t_1r^8}{t_1r^3}=\frac{5x^{20}}{8x^3}\] Then use any of the before equations t_4 or t_9 to find t_1. At last, you should do t_n=t_1*r^{n-1}.
Try it.

Answer 6

However, the solution you give is not the correct solution for the problem you posted. You can check it. With the solution you give,
\[t4=8\cdot x^3\\
t9=256\cdot x^8\]
So or the problem is wrong or the solution is wrong.