Question

Find an equation for the nth term of a geometric sequence where the second and fifth terms are -8 and 512, respectively.

a. an = 2 • (-4)n + 1
b. an = 2 • 4n - 1
c. an = 2 • (-4)n - 1
d. an = 2 • 4n

Answer 1

easy
recall that
an=a1(r)^(n-1)
so

given 2nd and 5th term

we get
a2 and a5
so
a2=a1(r)^(2-1)=a1(r)^1=a1r
a5=a1(r)^(5-1)=a1(r)^4

also remember that
`(x^m)/(x^n)=x^(m-n)`
so

`(a_5)/(a_2)= (a_1r^4)/(a_1r^1) =r^(4-1)=r^3= (512)/(-8)=-64`
so r^3=-64
cube root
r=-4
so

a2=a1r=-8
a2=a1(-4)=-8
divide both sides by -4
a1=2

so

equation is

`a_n=2(-4)^(n-1)`

C isi the answer