23.8k views
0 votes
What are the explicit equation and domain for a geometric sequence with a first term of 2 and a second term of -8

User Kyle W
by
8.0k points

2 Answers

7 votes

Answer:


\large\boxed{a_n=2(-4)^(n-1)=((-4)^n)/(2)}

Explanation:

The explicit equation of a geometric sequence:


a_n=a_1r^(n-1)

The domain is the set of all Counting Numbers.

We have the first term of
a_1=2 and the second term of
a_2=-8.

Calculate the common ratio r:


r=(a_(n-1))/(a_2)\to r=(a_2)/(a_1)

Substitute:


r=(-8)/(2)=-4


a_n=(2)(-4)^(n-1)\qquad\text{use}\ (a^n)/(a^m)=a^(n-m)\\\\a_n=(2\!\!\!\!\diagup^1)\left(((-4)^n)/(4\!\!\!\!\diagup_2)\right)\\\\a_n=((-4)^n)/(2)

User CCSJ
by
7.8k points
2 votes

Answer:

Explanation:

A geometric sequence has a common ratio. in this case the common ratio

r = -8/2 = -4.

The explicit formula is an = 2(-4)^(n-1).

User Thaw De Zin
by
8.4k 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