We want to determine whether the given sequence is a geometric sequence. To do so, we will calculate the ratio between consecutive terms.
We can see that there is a common ratio, r= - 12. Therefore, the sequence is geometric. To write the recursive and explicit formulas, we also need to identify the starting value. The first value given is 200. Now, let's write the formulas!
c|c
Explicit Formula & Recursive Formula [0.8em]
a_n= a_1 * r^(n-1) & a_1= a;
& a_n=a_(n-1) * r
↓ & ↓
& a_1= 200 ;
a_n= 200 * ( - 1/2)^(n-1) & a_n=a_(n-1) * ( - 1/2)
