The fourth term is 8
Step-by-step explanation:
Given
s-4 = 65
r = 2/3
n = 4
We know that the formula for finding the sum of finite geometric series is:
[tex]S_n = \frac{a_1(1-r^n)}{1-r}[/tex]
Putting the values of S and n
[tex]65 = \frac{a_1(1-(\frac{2}{3})^4)}{1-\frac{2}{3}}\\65 = \frac{a_1(1-\frac{16}{81})}{1-\frac{2}{3}}\\65 = \frac{a_1(\frac{81-16}{81})}{\frac{3-2}{3}}\\65 = \frac{a_1(\frac{65}{81})}{\frac{1}{3}}\\65 = a_1 * \frac{65}{81} * 3\\65 * \frac{81}{65} * \frac{1}{3} = a_1\\a_1 = 27[/tex]
The explicit formula for geometric sequence is:
[tex]a_n = a_1 * r^{n-1}[/tex]
Putting the values
[tex]a_n = 27 * (\frac{2}{3})^{n-1}[/tex]
Putting n=4
[tex]a_4 = 27 * (\frac{2}{3})^{4-1}\\a_4 = 27 * (\frac{2}{3})^3\\a_4 = 27 * \frac{8}{27}\\a_4 = 8[/tex]
The fourth term is 8
Keywords: Geometric sequence, Common ratio
Learn more about geometric sequence at:
- brainly.com/question/11007026
- brainly.com/question/11207748
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