Arithmetic Sequences Graphs

Fill in the blanks: Arithmetic sequences are graphed as _________ functions.

• Linear

• Exponential

Is this a graph of an arithmetic or a geometric sequence?

• Arithmetic

• Geometric

Is this sequence arithmetic, geometric, or neither?
{26, 22, 18, 14, ...}

• Arithmetic

• Geometric

• Neither

What is the common difference for the sequence shown?

• -4

• 3

• -1

• 1

Which function represents the sequence?

• f(n) = n + 3

• f(n) = 7n - 4

• f(n) = 3n + 7

• f(n) = n + 7

Answer explanation

Just think of the pattern as if it was a table!

----- ----- ----- -----

Final answer will look like:

f(n) = a₀ + (d)(n)

----- ----- ----- -----

Step 1: Find "d"

Subtract a_n values backwards

I will pick last two numbers

d = 31 - 24 = 7

----- ----- ----- -----

Step 2: Find "a₀"

Only one answer choice has correct "d" value so we don't need to find "a₀" value here

----- ----- ----- -----

f(n) = -4 + 7n

f(n) = 7n - 4

Which function represents the sequence?

• f(n) = n + 3

• f(n) = 7n - 4

• f(n) = 3n + 7

• f(n) = n + 7

Answer explanation

Final answer will look like:

f(n) = a₀ + (d)(n)

----- ----- ----- -----

Step 1: Find "d"

Subtract a_n values backwards

I will pick last two numbers

d = 31 - 24 = 7

----- ----- ----- -----

Step 2: Find "a₀"

Only one answer choice has correct "d" value so we don't need to find "a₀" value here

----- ----- ----- -----

f(n) = -4 + 7n

f(n) = 7n - 4

Which two functions represent the sequence?

• f(n) = n + 3

• f(n) = 7n - 4

• f(n) = 3 + 7(n - 1)

• f(n) = 7 + 3(n - 1)

Answer explanation

Final answer will look like:

f(n) = a₀ + (d)(n)

f(n) = a₁ + (d)(n - 1)

----- ----- ----- -----

We already found one answer

f(n) = a₀ + (d)(n)

f(n) = -4 + 7n

----- ----- ----- -----

Find second answer

f(n) = a₁ + (d)(n - 1)

f(n) = 3 + 7(n - 1)

Which function represents the sequence?

• f(n) = 3n + 3

• f(n) = 3n + 0

• f(n) = n + 3

• f(n) = n + 3

Answer explanation

Just think of the pattern as if it was a table!

----- ----- ----- -----

Final answer will look like:

f(n) = a₀ + d(n)

----- ----- ----- -----

Step 1: Find "d"

Subtract sequence values backwards

I will pick last two numbers

d = 15 - 12 = 3

----- ----- ----- -----

Step 2: Find "a₀"

Work backwards to find f(0)

f(0) = f(1) - (d)

f(0) = (3) - (3) = 0

----- ----- ----- -----

f(n) = 0 + 3n

f(n) = 3n + 0

Which function represents the sequence?

• f(n) = 3n + 3

• f(n) = 3n + 0

• f(n) = n + 3

• f(n) = n + 3

Answer explanation

Final answer will look like:

f(n) = a₀ + d(n)

----- ----- ----- -----

Step 1: Find "d"

Subtract sequence values backwards

I will pick last two numbers

d = 15 - 12 = 3

----- ----- ----- -----

Step 2: Find "a₀"

Work backwards to find f(0)

f(0) = f(1) - (d)

f(0) = (3) - (3) = 0

----- ----- ----- -----

f(n) = 0 + 3n

f(n) = 3n + 0

Which two functions represent the sequence?

• f(n) = 3n + 3

• f(n) = 3n + 0

• f(n) = 3 + 3(n - 1)

• f(n) = n + 3

Answer explanation

Final answer will look like:

f(n) = a₀ + d(n)

f(n) = a₁ + d(n - 1)

----- ----- ----- -----

We already found one answer

f(n) = a₀ + d(n)

f(n) = 0 + 3n

----- ----- ----- -----

Find second answer

f(n) = a₁ + d(n - 1)

f(n) = 3 + 3(n - 1)