Step-by-step explanation:
geometric sequence means that every term is created by multiplying the previous term by a constant factor.
we can see the constant factor directly, I am sure, but let's do it formally correct :
-1/8 × f = -1/4
f = -1/4 / -1/8 = -1/4 × -8/1 = -8/-4 = 2
so, yes, every new term of the sequence is created by multiplying the previous term by 2.
a0 = -1/8
a1 = a0 × 2 = -1/8 × 2 = -2/8 = -1/4
a2 = a1 × 2 = a0 × 2×2 = -1/8 × 2×2 = -1/8 × 4 = -4/8 = -1/2
...
an = a0 × 2^n = -1/8 × 2^n
a6 = -1/8 × 2⁶ = -1/8 × 64 = -8
so, the only questing is, where does your teacher start the count for such a geometric sequence ?
do you call the first term a0 or a1 ?
my solution above starts with a0.
but if it should start with a1, then we need to reduce the exponents of 2 by 1 :
an = -1/8 × 2^(n-1)
and a6 would be
a6 = -1/8 × 2⁵ = -1/8 × 32 = -4
