Question

Find an explicit rule for the nth term of a geometric sequence where the second and fifth terms are -36 and 2304, respectively.

Answer 1

an = 9 • 4^n
an = 9 • 4^(n - )
an = 9 • (-4)^)n + 1)
an = 9 • (-4)^(n - 1)

Answer 2

Do you know the formula for a geometric series?

Answer 3

sorry sequence?

Answer 4

I do not

Answer 5

What is it?@peachpi

Answer 6

\[a _{n}=a _{1}r ^{n-1}\]
a1 = first term and r = common ratio

Answer 7

since we have the second term we can write
\[-36=a _{1}r ^{2-1}=a _{1}r\]

Answer 8

Can you write the equation for the 5th term?

Answer 9

2304 = a1r^2 = a1r

?

Answer 10

@peachpi

Answer 11

Since it's the 5th term, the exponent is 5-1 = 4

Answer 12

2304 = a1 * r^4

Answer 13

make sense?

Answer 14

Yes

Answer 15

So now you have two equations and two unknowns. You can use substitution to solve the system

Answer 16

-36 = a1*r
r = 36/a1
Substitute into the 2304 equation