A1: Lesson 10.1: Arithmetic Sequence

A1: Lesson 10.1: Arithmetic Sequence

By Patrick Moseley

Multiple Choice

Given the following sequence:

7, 10, 13, 16, ...

Is there a arithmetic pattern?

• Yes

• No

Fill in the Blanks

Easy identification of pattern:

Second term minus the first one. Does this hold up between the rest of the terms?

If yes, then d=#.

Given the following sequence:

7, 10, 13, 16, ...

What is the pattern?

d =

Multiple Choice

Given the following sequence:

4, 7, 9, 12, ...

Is there a arithmetic pattern?

• Yes

• No

​Given the following sequence:

4, 7, 9, 12, ...

Is there a arithmetic pattern?

​

​

Sometimes...there is NO pattern.

Multiple Choice

Given the following sequence:

15, 13, 11, 9, ...

Is there a pattern and if so what is the common difference?

• Yes, d = 1/2

• Yes, d = 2

• Yes, d = -2

• No Pattern

Multiple Choice

Given the following sequence:

-9, -14, -19, -24, ...

Is there a pattern and if so what is the common difference?

• Yes, d = 1/5

• Yes, d = 5

• Yes, d = -5

• No Pattern

​Finding specific terms from an arithmetic sequence:

formula: a_n = d(n - 1) + a¹

a₁: first term in the sequence

d: common difference

n: the term location you want to calculate

Example:

Given: -1, -4, -7, -10, ...

a₁ = -1 and d = -3​

​

Formula: ​a₁=-3n+2

​

Replace the n for the desired term needing to calculate.​

Fill in the Blanks

Given: -1, -4, -7, -10, ...

a₁ = -1 and d = -3​

​

Formula: ​a₁=-3n+2

Calculate a₂₄ =

Multiple Choice

Given: -4, -9, -14, -19, ...

What formula would you use to calculate the n^th term?

• a_n = n +

• a_n = -5n + 1

• a_n = n - 5

• a_n = -2n + 1

Fill in the Blanks

Given: -4, -9, -14, -19, ...

Calculate a₂₄ =

Fill in the Blanks

Given: 7, 13, 19, 25, ...

Calculate a₂₄ =

​Working With Scenarios:

You visit the Grand Canyon and drop a penny off the edge of the cliff. The Distance the penny will fall is 16 feet for the first second, 48 feet feet the next second, 80 feet the third second, and so on.

​

First: Record this sequence:

16,48,80,...​

​

​Next: Write an equation:

​ a₁ = 16 and d = 32

a_n = 32n - 16​

​

Predict the distance a penny falls at six seconds: 176 feet

Fill in the Blanks

As manager f the soccer team, Wendy is to hand out cups of water at practice. Each cup of water is 4 ounces. She begins practice with a 128 ounce cooler of water. How much water is left after the 14^th cup?