help pleaseeeee

Question

which choice is the explicit formula for the following geometric sequence? 0.2,-0.06,0.018,-0,0054,0.00162,...

Answer 1

-.06/.2 = -.3 = r = the common ratio

an = a1(r)^(n-1) = 0.2(-0.3)^(n-1)

a(-1) = a1(r)^-2 = .2/.09 = 20/9

a0 = a1(r)^-1 = a1/-.3 = -2/3

a1 = a1(r)^0 = a1 = .2

a2 = a1(r)^1 = a1(-0.3) = -0.06

a3 = a1(r)^2 = a1(0.9) - 0.018

a4 =a1(r)^3 = a1(-0.27)= -0.0054

a5 =a1(r)^4 = a1(0.081) = 0.00162

a6 = a1(r)^5 = a1(-0.0243) = -0.00486

a7 = a1(r)^6 = a1(0.00729) = 0. 002187

an = 0.2(-0.3)^(n-1)

r has to be negative because the terms alternate in sign

r = the ratio of any term over its preceding term. = an/(an-1) = a(n+1)/an =a7/a6 = a6/a5 a5/a4 = a4/a3 = a3/a2 = a2/a1 = a1/a0 = a0/a(-1)

It's only a geometric sequence if the ratio is the same for each term divided by its preceding term