Arithmetic and Geometric Sequences

Arithmetic and Geometric Sequences

Putting It All Together!

Open Ended

What is the difference between an arithmetic and a geometric sequence?

Multiple Select

Identify which sequences are arithmetic:

• -16, -6, 4, 10...

• -2, 10, -50, 250...

• 28, 26, 24, 22...

• 4, 7, 10, 14...

Explicit Function Notation for Arithmetic Sequences

• Identify the common difference "d"

• Use the common difference to find the a₀ term

• Substitute these values into f(n) = dn + a₀

• "n" represent the term's location (position) in the sequence

• f(n) represents the value of that n term

Fill in the Blank

Write the explicit function for the following arithmetic function:

-40, -47, -54, -61...

Multiple Select

Identify which of the following sequences are geometric:

• 162, 108, 72, 48...

• 34, 43, 52, 61...

• 1, -1, 1, -1, 1...

• -1, 6, 36, 216...

Explicit Functions for Geometric Sequences

• Identify the common ratio "r"

• "r" must be written as multiplication

• To find a₀, divide a1 by the "r" value

• Substitute the r and a0 into the function f(n) = a₀ X rⁿ

Fill in the Blank

Write the explicit function for the following geometric sequence:

-15, 75, -375, 1875...

Recursive Function Notation for Arithmetic Sequences

• a_n = current term

• a_n-1 = previous term

• a_n+1 = next term

• a₁ = _____ must always be listed

Recursive Function Notation continued

• a_n = a_n-1 + d a₁ = ______

• Replace only the "d"...(common difference)

• You must always identify the a₁ (starting term)

Multiple Choice

True or False:

The recursive function allows you to find any term in the sequence??

• False

• True

Fill in the Blank

Write the Recursive Function for the following sequence

39, 32, 25, 18...

Open Ended

Given the following function, identify the first 5 terms

 $a_n=\ a_{n\ }-_1\ +\ 6$   $a_1\ =\ 4$  

Multiple Choice

Which is the correct notation for the recursive function for geometric sequences?

• $a_n=r\ \times\ a_n-_1$

• $a_{n_{ }}=\ r\ \times a_n-_1\ \ \ \ \ a_{1\ }=_{ }$

Multiple Choice

What would the graph of an arithmetic sequence look like?

• If connected the dots would be linear

• If connected the dots would curve

Multiple Choice

What are the first 4 terms of an arithmetic sequence with a common difference of (-6) if the first term is 76?

• 76, 70, 64, 58
• 76, 82, 88, 94
• 70, 64, 58, 52
• 82, 88, 94, 100

Multiple Choice

The individual numbers in a sequences are called...

• Common difference
• Successive term
• Term
• Geometric term

Multiple Choice

What kind of sequence is the pattern 400, 200, 100, 50, 25, ...?

• Arithmetic
• Geometric
• Neither

Multiple Choice

What is the 15th term of the sequence an = -3n+50

• 95
• -5
• 5
• -95

Multiple Choice

Identify the common difference.
97, 86, 75, 64, ...

• 8
• 11
• -11
• -8

Multiple Choice

Find the first term of the given sequence:
a₁₄=68
d=3

• 14
• 20
• 26
• 29

Multiple Choice

Find the 22nd term of the following sequence:
5, 8, 11, ...

• 14
• 68
• 63
• 71