Question

PLEASE HELP IF YOU CAN!
What is the explicit rule for the arithmetic sequence shown in the graph?
$an=-23+2(n-1)$
$an=-2.75+0.5(n-1)$
$an=9.5+2(n-1)$
$an=11+0.5(n-1)$

Answer 1

$\bf \begin{array}{ccllll} term&value\\ \textendash\textendash\textendash\textendash\textendash\textendash&\textendash\textendash\textendash\textendash\textendash\textendash\\ a_1&9.5\\ a_2&11.5\\ a_3&13.5\\ a_4&15.5\\ ...&... \end{array}\\\\ -----------------------------\\\\ a_n=a_1+(n-1)d\qquad \begin{cases} n=n^{th}\ term\\ a_1=\textit{first term}\\ d=\textit{common difference} \end{cases}$

notice, the first term is 9.5
from there it goes to 11.5, well, how much is it being added to get 11.5?
well 9.5 + 2, is 11.5, so it was added 2 to 9.5

then it goes from 11.5 to 13.5, namely, 11.5+2 = 13.5
and then 13.5+2 = 15.5 and so on

so, the "common difference" or the common addition value, is 2
how do you find the nth term?

well  $\bf a_n=9.5+(n-1)2\iff a_n=9.5+2(n-1)$

Answer 2

The explicit rule for the arithmetic sequence shown in the graph is  Tn = 9.5 + (n - 1)2

What is an arithmetic sequence?

Sequences are numbers arranged in a particular pattern. Given the arithmetic sequence shown in the graph as;

9.5, 11.5, 13.5, 15.5,...

The explicit form of the sequence is expressed as:

Tn = a + (n - 1)d

d is the common difference  = 11.5 - 9.5

d = 2

a is the first term = 9.5

Substitute

Tn = 9.5 + (n - 1)2

Tn = 9.5 + 2n - 2

Tn = 2n - 7.5

Hence the explicit rule for the arithmetic sequence shown in the graph is  Tn = 9.5 + (n - 1)2

Learn more on sequences here: https://brainly.com/question/6561461