Arithmetic Sequences and Explicit Formulas

FYI, The picture is an example of the **explicit formula**

What does the -3 represent?

• The constant rate of change

• The y-intercept

• An x-value

Tags

CCSS.HSF.BF.A.2

What does the 10 represent?

• The constant rate of change

• When the nth term is zero (the zero term)

• An x-value

Tags

CCSS.HSF.BF.A.2

What is: A list of numbers that increase or decrease by a constant rate

• Geometric sequence

• positive sequence

• negative sequence

• Arithmetic sequences

Tags

CCSS.HSF.BF.A.2

Is this an arithmetic sequence?

• Maybe

• Yes

• No

Answer explanation

The rate is not constant, which is required in arithmetic sequences.

So no, its not arithmetic

Tags

CCSS.HSF.BF.A.2

What two things do you need to write the explicit formula? (Choose two and look carefully)

• the last term

• The zero term (when x=0)

• Constant rate

• changing rate

Answer explanation

You need to find the rate of how the y's change, and then find the f(x) value when x is zero.

Tags

CCSS.HSF.BF.A.2

**This question requires some thinking**

If the first term (when n=1) of a sequence is 7 and the common difference is 6, what is the explicit formula?

(take your time)

• a_n = 7n - 6

• a_n = 6n - 7

• a_n = 7n + 6

• a_n = 6n + 1

Answer explanation

When n=1, the value is 7. But we need to find when n=0. So, just subtract 7 by 6 (the rate) to find n=0

Tags

CCSS.HSF.BF.A.2

How do you feel so far about the topic?

• Good!

• Um... not so good

• Bad

Answer explanation

Dont worry, we will work on this more. Don't rush, and read the question carefully

What is the rate of this arithmetic sequence?

• -2

• 2

• 1

• 14

Tags

CCSS.HSF.BF.A.2

What is the zero term (a_0) of this arithmetic sequence? (hint**you have to find it)

• -2

• -1

• 1

• -2

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CCSS.HSF.BF.A.2

Now we know:

zero term= -1

Constant rate= 2

Which explicit formula fits this scenario?

• a_n = -1n + 2

• a_n = 2n - 1

• a_n = n - 1

• a_n = 2n + 1

Tags

CCSS.HSF.BF.A.2