a We want to find the first five terms of the given geometric sequence. Let's identify the starting value a_1 and the common ratio r.
la_1= 5 a_n= - 2 * a_(n-1)
We see that the starting value is a_1= 5. The common ratio of the sequence is r= - 2. It means that the ratio between any two consecutive terms is - 2. Let's use this information to write the first five terms of the sequence.
la_1= 5 a_n= - 2 * a_(n-1)
From Part A we already know that the starting value is a_1= 5, and the common ratio of the sequence is r= - 2. With these values, we can write the explicit formula.
Explicit formula [0.8em]
a_n= a_1 * r^(n-1)
↓
a_n= 5 * ( - 2 )^(n-1)
