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ziro4ka [17]
3 years ago
6

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

Mathematics
1 answer:
Virty [35]3 years ago
5 0

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.

----

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.

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