write an equation for the nth term of the geometric sequence 3,-24,192

Question

 find nth term

Answer 1

Hi Haley,

 

In words the nth term of a geometric sequence is the first term multiplied by (n-1) times the common ratio.

 

The formula looks like this:

 

a_n = a₁(r)^(n-1)

 

For your problem a₁ = 3, the first term. What is r? Divide any term by the term that precedes it: -24/3 = -8. 

 

So, a_n = 3(-8)^(n-1)

 

Convince yourself by solving for a₂ (the second term):

 

a₂ = 3 (-8)^(2-1) = 3(-8) = -24

 

How about a₃ = 3(-8)^{(3 - 1)} = 3(-8)² = 3(64) = 192. 

 

Try a₆ and see what you get.