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

To find t4 in the geometric sequence tn with t1 = 96 and r = -1/4, we can use the formula tn = t1 * r^(n-1). Substituting the values and solving, t4 = -3/2.

Step-by-step explanation:

To find the value of t4 in the given geometric sequence, we can use the formula for the nth term of a geometric sequence: tn = t1 * r^(n-1).

Given that t1 = 96 and r = -1/4, we can substitute these values into the formula to find t4 as follows:

t4 = 96 * (-1/4)^(4-1)

t4 = 96 * (-1/4)^3

t4 = 96 * (-1/64)

t4 = -3/2

Therefore, t4 = -3/2.