Question

Given the Table Circle One: Arithmetic, Geometric, or NeitherCircle One: Common Ratio or Common Difference Write the Recursive Formula-Write the Explicit Formula- Find the 10th term-

Answer 1

Given the table:

x y

1 2

2 0

3 -2

4 -4

Difference between x values:

4 - 3 = 1

3 - 2 = 1

2 - 1 = 1

Difference between y values:

-4 - - 2 = -4 + 2 = -2

-2 - - 0 = - 2 + 0 = -2

0 - 2 = -2

This table represents an Arithmetic sequence.

An arithmetic sequence is a sequence that has a constant difference between the terms.

From the table given, the difference between the consecutive terms is constant.

We have:

First term = 2

Second term = 0

Third term = -2

Fourth term = -4

Arithmetic sequence has a common difference.

The common difference = -2

Use the arithmetic sequence formula:

`a_n=a_1+(n-1)d`

Where:

a1 = first term

n = number of terms

d = common difference

To write the recursive formula, we have:

`\begin{cases}a_1=2 \\ a_n=a_(n-1)_{}-2\end{cases}`

To write the explicit formula, we have:

`a_n=2_{}+(n-1)(-2)`

Let's simplify the explicit formula:

`\begin{gathered} a_n=2+(n-1)(-2) \\ \\ a_n=2+\text{ n(-2) -1(-2)} \\ \\ a_n=2-2n+2 \\ \\ a_n=-2n+2+2 \\ \\ a_n=-2n+4 \end{gathered}`

To find the 10th term, let's use the explicit formula.

Substitute 10 for n

`\begin{gathered} a_(10)=-2(10)+4 \\ \\ a_(10)=-20+4 \\ \\ a_(10)=-16 \end{gathered}`

Therefore, the 10th term of the arithmetic sequence is -16

ANSWER:

Arithmetic Sequence

Common difference

Recursive formula:

`\begin{cases}a_1=2 \\ a_n=a_(n-1)-2\end{cases}`

Explicit formula:

`a_n=-2n+4`