188k views
4 votes
Write an explicit rule for the recursive rule. a1=−2,an=9an−1

User Eluong
by
8.7k points

1 Answer

4 votes

Answer:


a_n=-2\cdot 9^(n-1).

Explanation:

You are given that


  • a_1=-2;

  • a_n=9a_(n-1).

Then


a_1=-2,\\ \\a_2=9a_1=9\cdot (-2)=-18,\\ \\a_3=9a_2=9\cdot (-18)=-162, \dots

Actually, this sequence is the geometric seequence with first term
a_1=-2 and ratio
r=9.

The explicit rule for the nth term of the geometric sequence is


a_n=a_1\cdot r^(n-1).

Hence,


a_n=-2\cdot 9^(n-1).

User Francis Bartkowiak
by
8.2k points

No related questions found

Welcome to QAmmunity.org, where you can ask questions and receive answers from other members of our community.

9.4m questions

12.2m answers

Categories