Answer:is: {a1=5an+1=−3an
Explanation: I assume the formula is: an=5(−3)n−1. To calculate the recursive formula first we can calculate some terms of the sequence: a1=5⋅(−3)1−1=5⋅(−3)0=5a2=5⋅(−3)2−1=5⋅(−3)1=−15a3=5⋅(−3)3−1=5⋅(−3)2=45From these calculations we see that the first term is a 1=5 and each other term comes from multiplying previous one by −3. This algorithm can be written as the recursive formula:{a1=5an+1=−3an