Answered

Identify the explicit function for the sequence in the table.

| [tex]$x$[/tex] | [tex]$y$[/tex] |
|----|----|
| 1 | 8 |
| 2 | 14 |
| 3 | 20 |
| 4 | 26 |
| 5 | 32 |

A. [tex]\( a(n) = 6(n-1) \)[/tex]
B. [tex]\( a(n) = 8 + (n-1) \cdot 6 \)[/tex]
C. [tex]\( a(n) = 6 + (n-1) \cdot 8 \)[/tex]
D. [tex]\( a(n) = 8(n-1) \)[/tex]



Answer :

GinnyAnswer
To identify the explicit function for the sequence in the table, we need to analyze the given values and determine the pattern. Let's examine the table:

[tex]\[ \begin{array}{|c|c|} \hline x & y \\ \hline 1 & 8 \\ \hline 2 & 14 \\ \hline 3 & 20 \\ \hline 4 & 26 \\ \hline 5 & 32 \\ \hline \end{array} \][/tex]

First, let's identify the common difference in the sequence of [tex]\( y \)[/tex] values:

[tex]\[ \begin{aligned} 14 - 8 &= 6, \\ 20 - 14 &= 6, \\ 26 - 20 &= 6, \\ 32 - 26 &= 6. \end{aligned} \][/tex]

We see that the difference between successive terms is constant and equals 6. This indicates an arithmetic sequence where the common difference [tex]\( d \)[/tex] is 6.

Next, we use the explicit formula for an arithmetic sequence:

[tex]\[ a(n) = a_1 + (n-1) \cdot d, \][/tex]

where [tex]\( a_1 \)[/tex] is the first term and [tex]\( d \)[/tex] is the common difference.

In this case:
- The first term [tex]\( a_1 = 8 \)[/tex].
- The common difference [tex]\( d = 6 \)[/tex].

Substituting these values into the formula, we get:

[tex]\[ a(n) = 8 + (n-1) \cdot 6. \][/tex]

So, the explicit function for the sequence is:

[tex]\[ a(n) = 8 + (n-1) \cdot 6. \][/tex]

Therefore, the correct answer is:

B. [tex]\( a(n) = 8 + (n-1) \cdot 6 \)[/tex].

Other Questions