The fourth term is: 192
Step-by-step explanation:
Given
sum of sequence = 16383
n = 7
r = 4
The formula for sum of finite geometric sequence is:
[tex]S_n = \frac{a_1(1-r^n}{1-r}\\Putting\ values\\16383 = \frac{a_1(1-4^7)}{1-4}\\16383 = \frac{a_1(1-16384)}{-3}\\16383 = \frac{a_1(-16383)}{-3}\\16383 = 5461a_1\\a_1 = \frac{16383}{5461}\\a_1 = 3[/tex]
The first term is 3
The general formula for geoetric sequence is:
[tex]a_n = a_1 . r^{n-1}[/tex]
Putting the value of r and a_1
[tex]a_n = 3.4^{(n-1)}[/tex]
Putting n=4
[tex]a_4 = 3. 4^{(4-1)}\\a_4 = 3.4^3\\=64*3\\=192[/tex]
Hence,
The fourth term is: 192
Keywords: Geometric sequence, common ratio
Learn more about geometric sequence at:
- brainly.com/question/4706270
- brainly.com/question/4710621
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