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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.

Respuesta :

MrRoyal

Answer:

3/2

Step-by-step explanation:

Given

[tex]t_1 = 96[/tex]

[tex]r = \frac{1}{4}[/tex]

Required

Find t4

The nth term of a geometric sequence is calculated as:

[tex]t_n = t_1 * r^{n-1[/tex]

So:

[tex]t_4 = t_1 * r^{4-1[/tex]

[tex]t_4 = t_1 * r^3[/tex]

This gives:

[tex]t_4 = 96 * \frac{1}{4}^3[/tex]

[tex]t_4 = 96 * \frac{1}{64}[/tex]

Express as a single fraction

[tex]t_4 = \frac{96}{64}[/tex]

[tex]t_4 = \frac{3}{2}[/tex]

Hence, the 4th term is 3/2

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