text: the first term of a geometric series is 2/5 and the sum of the first nine terms is 511/640....help? and the common ratio is positive, what is the common ratio using formulas? ok here it goes, so first the formula is s(n)=a(1-r^n) all over 1-r  sub 511/640 = 2/5 * (1-r^9) all over 1-r multiply both sides by 5/2 to make one side variables only that will become 511/256= 1-r^9 all over 1-r cross multiply 511-511r=256-256r^9  arrange it 256r^9-511r+255=0 (256r^3-255)(r^3-1)=0 r= cube root of 1 or just simply one. but it can't be one cause when u sub it it won't be 511/640 neither -1. so get the cube root of 255/256 so the answer would be  cube root of 510 over 8