Answer :
Step-by-step explanation:
a geometric sequence means that there is a constant factor r (the common ratio) that is multiplied to one term of the sequence to create the next one :
an = an-1 × r
and that all starts with a starting value a1.
a2 = a1 × r
a3 = a2 × r = (a1 × r) × r = a1 × r²
...
and we see that
an = a1 × r^(n-1)
that is the explicit formula.
so, we need to find a1 and r, 2 variables. luckily we get also 2 cases (n = 4 and n = 9) to solve for these 2 variables.
-192 = a1 × r³
196608 = a1 × r⁸
from the first we get e.g.
a1 = -192/r³
using that in the second equation :
196608 = (-192/r³) × r⁸ = -192 × r⁵
196608/-192 = r⁵
-1024 = r⁵
r = -4
a1 = -192/r³ = -192/-64 = 3
and so, the explicit formula is
an = 3 × (-4)^(n-1)
