Write a rule for the nth term of the geometric sequence with terms: a(1) = -6, a(4) = 48

Question

a) a_n = -6(-2)^n-1

b) a_n = -6(-1/2)^n-1

c) a_n = -6(2)^n-1

d) a_n = -6(1/2)^n-1

Answer 1

The form of a geometric sequence is a_n=a₁(r)^n-1

For this sequence, a₁, the first term is -6.

We need to figure out the common ration, r

a₂ = (-6)(-2) = 12

a₃ = (12)(-2) = -24

a₄ = (-24)(-2) = 48

r=-2 gives us the correct a₄ term. So the solution is

a) a_n=-6(-2)^n-1