Question

Find an equation for the nth term of a geometric sequence where the second and fifth terms are -2 and 16, respectively.

Answer 1

do u know the general equation for a geometric series?

Answer 2

is it xn = ar(n-1)

Answer 3

yep, or \[a_n = a_1 \times r^{n-1}\], if u prefer x as the term that's cool too

so the question says that the 2nd term is -2
so \[a_2 = a_1 \times r^{2-1}\] = -2

and the fifth term is 16
so \[a_5 = a_1 \times r^{5-1}\] = 16
so we can use elimination to solve for a_1

Answer 4

so it's an = 1 • (-2)^n - 1

Answer 5

*substitution* not elimination
a2 = -2 = a1 x r^1
so a1 = -2/r

sub that into
a5 = 16 = a1 x r^4

Answer 6

yep perfect,
r = -2
a1 = 1

Answer 7

Thank You !