1. ## geometric sequence

Find a, r, and Tn for each geometric sequence
a)t4=24 and t6=96 b)t2=-6 and t5=-162
-thank you for whoever answers my question .......

2. Originally Posted by polymerase
Find a, r, and Tn for each geometric sequence
a)t4=24 and t6=96
a)$\displaystyle t_4 =24$ and $\displaystyle t_6 = 96$

In general
$\displaystyle t_n = t_1 \cdot r^{n - 1}$

We have
$\displaystyle t_4 = t_1 \cdot r^3 = 24$
$\displaystyle t_6 = t_1 \cdot r^5 = 96$

Thus
$\displaystyle \frac{t_6}{t_4} = \frac{96}{24} = r^2$

or

$\displaystyle r^2 = 4$

Thus $\displaystyle r = \pm 2$

Take r = 2:
$\displaystyle t_4 = 24 = t_1 \cdot (2)^3 = 8t_1$

Thus $\displaystyle t_1 = 3$ and $\displaystyle t_n = 3(2)^{n - 1}$

Take r = -2:
$\displaystyle t_4 = 24 = t_1 \cdot (-2)^3 = -8t_1$

Thus $\displaystyle t_1 = -3$ and $\displaystyle t_n = -3(-2)^{n - 1}$

Both series will produce the correct terms.

-Dan

3. Originally Posted by polymerase
Find a, r, and Tn for each geometric sequence
b)t2=-6 and t5=-162
Follow the same steps as before.
$\displaystyle t_n = t_1 \cdot r^{n - 1}$

with
$\displaystyle t_2 = -6 = t_1 \cdot r$
$\displaystyle t_5 = -162 = t_1 \cdot r^4$

Dividing I get that
$\displaystyle r = 3$

and from there I get that
$\displaystyle t_1 = -2$

Thus
$\displaystyle t_n = -2(3)^{n - 1}$

-Dan