Consider the following sequence: \{8,\ -24,\ 72,\ -216,\ 648\} It this an geometric sequence?

Amari Flowers

Amari Flowers

Answered question

2021-07-31

Consider the following sequence:
{8, 24, 72, 216, 648}
It this an geometric sequence?
a) The squence is geometric. The common ratio is: r=?
b) The sequence is arithmetic.
c) The sequence is neither geometric nor arithmetic.

Answer & Explanation

gotovub

gotovub

Skilled2021-08-01Added 98 answers

Step 1
Given sequence,
8, 24, 72, 216, 648
The general form of geometric sequence is
a, ar, ar2, ar3, ar4, 
For the sequence, the ratio of the consecutive terms is constant is known as geometric sequence and the constant term is common ratio r.
r=an+1an, n1
Step 2
a2a1=248=3
a3a2=7224=3
a4a3=21672=3
a5a4=648216=3
As we can see the ratio of the consecutive term is constant, thus the given sequence is geometric with common ratio 3.
Step 3
Therefore,
The given sequence is geometric.
The common ratio is:
r=3
Thus, 1st option is correct.
Jeffrey Jordon

Jeffrey Jordon

Expert2022-07-06Added 2605 answers

Answer is given below (on video)

2022-08-30

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