Question

Determine whether each set of ordered pairs shown below is from a geometric sequence or from an arithmetic sequence.

{(-3, 7.5) , (-2, 10) , (-1, 12.5)}

Write the equation of the graph for the set of ordered pairs.

{(1, 150) , (2, 112.5) , (3, 84.375)}

Write the equation of the graph for the set of ordered pairs.

Answer 1

Using sequences concepts, it is found that:

• The set of ordered pairs {(-3, 7.5) , (-2, 10) , (-1, 12.5)} is an arithmetic sequence with equation a(n) = 15 + 2.5d.

• The set of ordered pairs {(1, 150) , (2, 112.5) , (3, 84.375)} is a geometric sequence with $a_n = 150(0.75)^{n-1}$.

What is an arithmetic sequence?

In an arithmetic sequence, the difference between consecutive terms is always the same, called common difference d.

The nth term of an arithmetic sequence is given by:

$a(n) = a(0) + nd$

The sequence {(-3, 7.5) , (-2, 10) , (-1, 12.5)} continues with points (0, 15), (1, 17.5), and so on, hence the first term and the common ratio are given, respectively, by:

a(0) = 15, d = 2.5.

Hence the equation is:

a(n) = 15 + 2.5n.

What is a geometric sequence?

A geometric sequence is a sequence in which the result of the division of consecutive terms is always the same, called common ratio q.

The nth term of a geometric sequence is given by:

$a_n = a_1q^{n-1}$

For the sequence {(1, 150) , (2, 112.5) , (3, 84.375)}, the first term and the common ratio are given, respectively, by:

$a_1 = 150, q = \frac{112.5}{150} = \frac{84.375}{112.5} = 0.75$

Hence the equation is given by:

$a_n = 150(0.75)^{n-1}$

More can be learned about sequences at https://brainly.com/question/6561461

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