MATH SOLVE

2 months ago

Q:
# Will give BRAINLIEST for the RIGHT answerFind A4 in the geometric series in which S4=65 and the common ratio is r=2/3

Accepted Solution

A:

The fourth term is 8Step-by-step explanation:Givens-4 = 65r = 2/3n = 4We 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 8Keywords: Geometric sequence, Common ratioLearn more about geometric sequence at:brainly.com/question/11007026brainly.com/question/11207748#LearnwithBrainly