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

Question

anonymous · Answer

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

anonymous · Answer

Do you know the formula for a geometric series?

anonymous · Answer

sorry sequence?

anonymous · Answer

I do not

anonymous · Answer

What is it?@peachpi

anonymous · Answer

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

anonymous · Answer

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

anonymous · Answer

Can you write the equation for the 5th term?

anonymous · Answer

2304 = a1r^2 = a1r

?

anonymous · Answer

@peachpi

anonymous · Answer

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

anonymous · Answer

2304 = a1 * r^4

anonymous · Answer

make sense?

anonymous · Answer

Yes

anonymous · Answer

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

anonymous · Answer

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