Geometric Progression

[anthropos]

The sum of the first 20 terms of a geometric series is 10 and the sum of the first 30 terms is 91, find the sum of the first 10 terms. Um please help me because I am stuck. Immediate help needed!

[dttom]

let the first term as a; the factor as r

a+...+ar^29=91

a(1-r^30)/(1-r)=91

a=91(1-r)/(1-r^30) ---(1)

a+...+ar^19=91

a(1-r^20)/(1-r)=91

a(1-r^20)=91(1-r)

91(1-r)(1-r^20)/(1-r^30)=91(1-r)

1-r^20=1-r^30

r^20=r^30

r=-1

a=91(2)/2=91

a+...+ar^9=a(1-r^10)/(1-r)

=91(0)/2=0