*I know it's already been answered, but I just wanted to add a different version of the steps. While this particular question could be answered in like 3 seconds, this method is a lot quicker when they want you to find 30th term lol
Answer:
500
Step-by-step explanation:
First, set up your equation:
a<em>n </em>= a<em>1 </em>* r ^ (n-1)
a<em>1 </em>is 2000, because it is the first term (4000 is the 0th term).
4000*(1/2)=2000.
a<em>n </em>= 2000<em> </em>* (1/2) ^ (<em>n-</em>1)
Now, subsitute <em>n </em>for 3:
a3<em> </em>= 2000<em> </em>* (1/2) ^ (3-1)
Solve:
a3 = 2000 * (1/2) ^ 2
a3 = 2000 * 0.25
a3 = 500