Answered

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.. :(

Verified Answer :

luana

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

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