Question

The explicit rule for the arithmetic sequence shown in the graph is a↓n=9.5+2(n-1)
True or False??

Answer 1

Answer:

True.

Step-by-step explanation:

The explicit form for an arithmetic sequence is:

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

where $a_1$ is the first term and $d$ is the common difference.

The common difference here is 2 because the y's are going up by 2 while the x's are going up by 1.

Yes, the common difference is the slope.

So we have d=2.

The first term is 9.5 because that is what happens when x=1.

x is n.

y is $a_n$.

So the answer is true.

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You can also verify by plugging in numbers for n and see if you get the outputs mentioned in the pairs given:

Let n=1:

$a_1=9.5+2(1-1)$

$a_1=9.5+2(0)$

$a_1=9.5+0$

$a_1=9.5$

Let n=2:

$a_2=9.5+2(2-1)$

$a_2=9.5+2(1)$

$a_2=9.5+2$

$a_2=11.5$

Let n=3:

$a_3=9.5+2(3-1)$

$a_3=9.5+2(2)$

$a_3=9.5+4$

$a_3=13.5$

Let n=4:

$a_4=9.5+2(4-1)$

$a_4=9.5+2(3)$

$a_4=9.5+6$

$a_4=15.5$

Let n=5:

$a_5=9.5+2(5-1)$

$a_5=9.5+2(4)$

$a_5=9.5+8$

$a_5=17.5$

Let n=6:

$a_6=9.5+2(6-1)$

$a_6=9.5+2(5)$

$a_6=9.5+10$

$a_6=19.5$

We have confirmed that we get all 6 of the mentioned points using the equation they gave.