Question

A geometric sequence is represented by a Subscript n Baseline = a Subscript 1 Baseline r Superscript n minus 1. What is the fifth term of a geometric sequence where a Subscript 1 Baseline = 4,096 and the common ratio is Negative one-fourth?

Answer 1

Answer:

16

Step-by-step explanation:

Given the nth term of a geometric sequence represented as $Tn = a_1r^{n-1}$

$a_1$ =  first term of the sequence

n = number of terms

r = common ratio

Given $a_1 = 4,096,\ r = -\frac{1}{4} , n = 5$(fifth term of the sequence)

$T_5 = 4,096(-\frac{1}{4} )^{5-1}\\ T_5 = 4,096(-\frac{1}{4} )^{4}\\T_5 = 4,096(\frac{1}{256} )\\T_5 = 16$

The fifth term of the geometric sequence is 16