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

True.

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.