Question

Which of the tables below contain values that would be considered an arithmetic sequence, and which contain values that would be considered a geometric sequence?

A. Arithmetic
B. Geometric
C. Neither

Answer 1

Table A represents an arithmetic sequence because the difference between each term is constant, while Table B represents a geometric sequence because each term is obtained by multiplying the previous term by a constant called the common ratio. Table C does not represent either an arithmetic or geometric sequence because the differences between consecutive terms are not constant.

Step-by-step explanation:

An arithmetic sequence is a sequence of numbers in which the difference between consecutive terms is constant. A geometric sequence is a sequence of numbers in which each term after the first is found by multiplying the previous term by a constant called the common ratio.

Looking at the tables, we can determine if they represent an arithmetic or geometric sequence by examining the differences between consecutive terms.

Table A:

1. 2
2. 5
3. 8

Table A represents an arithmetic sequence because the difference between each term is 3, which is constant.

Table B:

1. 2
2. 6
3. 18

Table B represents a geometric sequence because each term is obtained by multiplying the previous term by 3, which is the common ratio.

Table C:

1. 2
2. 4
3. 7

Table C does not represent either an arithmetic or geometric sequence because the differences between consecutive terms are not constant.