Question

Given the geometric sequence tn with t1=96 and r=−1/4, find t4.

Give your answer as a fraction, if necessary. Do not include "t4=" in your answer. For example, if you found t4=9, you would enter 9.

Answer 1

Answer:

3/2

Step-by-step explanation:

Given

$t_1 = 96$

$r = \frac{1}{4}$

Required

Find t4

The nth term of a geometric sequence is calculated as:

$t_n = t_1 * r^{n-1$

So:

$t_4 = t_1 * r^{4-1$

$t_4 = t_1 * r^3$

This gives:

$t_4 = 96 * \frac{1}{4}^3$

$t_4 = 96 * \frac{1}{64}$

Express as a single fraction

$t_4 = \frac{96}{64}$

$t_4 = \frac{3}{2}$

Hence, the 4th term is 3/2