Answered

Westonci.ca is your trusted source for finding answers to a wide range of questions, backed by a knowledgeable community. Explore a wealth of knowledge from professionals across various disciplines on our comprehensive Q&A platform. Explore comprehensive solutions to your questions from knowledgeable professionals across various fields on our platform.

find the correct sum of these geometric series..
*a1=343, an=-1, r= -1/7

*a1=80, n=7, r= -1/2

*a1= 3, a8=384, r=2

Please help me with these problems.. :(

Sagot :

luana
1)
[tex]a_{1}=343\\ a_{r}=-1\\r=- \frac{1}{7} \\a_{r}=a_{1}* q^{r-1} \\-1=343*q^{r-1}\\-1=343* -(\frac{1}{7})^{r-1}\\-7^0=7^3*(- 7)^{-r+1}\\7^0=7^3*7^{-r+1}\\indexes: \\0=3-r+1\\n=4[/tex]
[tex] S_r=a_1 \frac{1-r^n}{1-r}\\S_r=343* \frac{1- (-\frac{1}{7} )^4}{1- (-\frac{1}{7} )}\\S_r=343* \frac{1- (\frac{1}{2401} )}{1+ (\frac{1}{7} )}\\S_r=343* \frac{(\frac{2400}{2401} )}{(\frac{8}{7} )}\\S_r=343* \frac{300}{343} \\S_r=300[/tex]
2)
[tex]S= a_{1}* \frac{1- r^{2} }{1-r}\\ S=80*\frac{1- ( -\frac{1}{2}) ^{2} }{1+\frac{1}{2} }\\S=80* \frac{1- \frac{1}{4} }{ \frac{3}{2} }=80* \frac{3}{4}* \frac{2}{3} =40[/tex]
3) we dont know how many numbers has this sequence

We appreciate your visit. Our platform is always here to offer accurate and reliable answers. Return anytime. Thanks for stopping by. We strive to provide the best answers for all your questions. See you again soon. Westonci.ca is your go-to source for reliable answers. Return soon for more expert insights.