Question

Complete the statement about the tables below. Then, choose a rule for each. x y 0 5 1 7.5 2 11.25 This table represents a(n) relationship. Rule: x y 0 -6 1 12 2 30 This table represents a(n) relationship. Rule:

Answer 1

Answer:

See below.

Step-by-step explanation:

First rule:-  Each value of y after the first one is obtained by multiplying the previous  value by 1.5, ( Note  11.25 / 7.5 = 1.5 and 7.5 / 5 = 1.5).

The relationship is  a(n) =  5 * 1.5^(n-1)

Second Rule:-   Note:-  12 - (-6) = 18 and 30 - 12 = 18.  So we add 18 to get the next term in this rule.

Relationship is a(n) = -6 + 18(n - 1).

Answer 2

The rule for the first table is a(n) = 5 × $(1.5)^(^n^-^1^)$  and the rule for the second table is a(n) = -6 + 18 (n-1). Since the first table represents a geometric sequence and the second table represents an arithmetic sequence of the data.

What are arithmetic and geometric sequences?

Geometric sequence:

• A geometric sequence is a sequence where the data values are related to a common ratio.
• The common ratio is the ratio of any data value to the previous data value.
• The general form of the nth term of a geometrical sequence is a(n) = a1 × $r^(^n^-^1^)$ where a1 is the first term in the sequence, r is the common ratio and n is the number of data items in the sequence.

Arithmetic sequence:

• An arithmetic sequence is a sequence where data values are related to a common difference.
• The common difference is the difference between any data term with the previous term.
• The general form of the nth term of an arithmetical sequence is a(n) = a1 × d(n-1) where a1 is the first term in the sequence, d is the common difference and n is the number of data items in the sequence.

Finding the relationships that the given tables show:

First table:

x: 0, 1, 2

y: 5, 7.5, 11.25

Finding the relationship between the data values of the given table,

7.5/5=1.5 and 11.5/7.5=1.5

Since the ratios of the terms are common, this is a geometric sequence. So, the relation is represented by the rule:

the first term is a1=5 and the common ratio r=1.5

Rule: a(n) = 5 × $(1.5)^(^n^-^1^)$

Second table:

x: 0, 1, 2

y: -6, 12, 30

Finding the relationship between the data values of the given table,

12 - (-6) = 18 and 30 - 12 = 18

Since the difference in the terms is common, this is an arithmetic sequence. So, the relation is represented by the rule:

the first term is a1= -6 and the common ratio d=18

Rule: a(n) = -6 + 18 (n-1)

So, the rule for the first table is a(n) = 5 × $(1.5)^(^n^-^1^)$  and the rule for the second table is a(n) = -6 + 18 (n-1).

Learn more about arithmetic and geometric sequences here:

https://brainly.com/question/13613396

#SPJ2