Question

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.. :(

Answer 1

1)

`a_(1)=343\\ a_(r)=-1\\r=- (1)/(7) \\a_(r)=a_(1)* q^(r-1) \\-1=343*q^(r-1)\\-1=343* -((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`

`S_r=a_1 (1-r^n)/(1-r)\\S_r=343* (1- (-(1)/(7) )^4)/(1- (-(1)/(7) ))\\S_r=343* (1- ((1)/(2401) ))/(1+ ((1)/(7) ))\\S_r=343* (((2400)/(2401) ))/(((8)/(7) ))\\S_r=343* (300)/(343) \\S_r=300`
2)

`S= a_(1)* (1- r^(2) )/(1-r)\\ S=80*(1- ( -(1)/(2)) ^(2) )/(1+(1)/(2) )\\S=80* (1- (1)/(4) )/( (3)/(2) )=80* (3)/(4)* (2)/(3) =40`
3) we dont know how many numbers has this sequence