EOC Functions (Sequences)

Sequences can be represented as lists, tables, graphs, or drawings.

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Which function represents the sequence?

(hint: the pattern is linear)

• 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!

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Final answer will look like:

f(n) = a₀ + (d)(n)

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Step 1: Find "d"

Subtract a_n values backwards

I will pick last two numbers

d = 31 - 24 = 7

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Step 2: Find "a₀"

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

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f(n) = -4 + 7n

f(n) = 7n - 4

Sequences can be represented as lists, tables, graphs, or drawings.

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Which function represents the sequence?

(hint: the pattern is linear)

• 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)

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Step 1: Find "d"

Subtract a_n values backwards

I will pick last two numbers

d = 31 - 24 = 7

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Step 2: Find "a₀"

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

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f(n) = -4 + 7n

f(n) = 7n - 4

Sequences can be represented as lists, tables, graphs, or drawings.

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Which two functions represent the sequence?

(hint: the pattern is linear)

• 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)

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We already found one answer

f(n) = a₀ + (d)(n)

f(n) = -4 + 7n

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Find second answer

f(n) = a₁ + (d)(n - 1)

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

Sequences can be represented as lists, tables, graphs, or drawings.

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

Which function represents the sequence?

(hint: the pattern is linear)

• 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!

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Final answer will look like:

f(n) = a₀ + d(n)

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Step 1: Find "d"

Subtract sequence values backwards

I will pick last two numbers

d = 15 - 12 = 3

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Step 2: Find "a₀"

Work backwards to find f(0)

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

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

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f(n) = 0 + 3n

f(n) = 3n + 0

Sequences can be represented as lists, tables, graphs, or drawings.

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

Which function represents the sequence?

(hint: the pattern is linear)

• 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

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f(n) = 0 + 3n

f(n) = 3n + 0

Sequences can be represented as lists, tables, graphs, or drawings.

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

Which two functions represent the sequence?

(hint: the pattern is linear)

• 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)

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We already found one answer

f(n) = a₀ + d(n)

f(n) = 0 + 3n

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Find second answer

f(n) = a₁ + d(n - 1)

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

Sequences can be represented as lists, tables, graphs, or drawings.

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Which is the value of the 44th term?

(hint: the pattern is linear)

Mathematical Equivalence

ON

Answer explanation

Find function, then solve:

f(n) = a₁ + (d)(n - 1)

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Step 1: Find "d"

Subtract y values backwards

I will pick last two numbers

d = 20 - 28 = -8

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Step 2: Find "a₁"

f(1) = 44 = a₁

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Step 3: Solve for n = 44

f(n) = a₁ + (d)(n - 1)

f(n) = 44 + (-8)(n - 1)

f(44) = 44 + (-8)(44 - 1)

f(44) = -300

Sequences can be represented as lists, tables, graphs, or drawings.

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Which function represents the sequence?

(hint: the pattern is exponential)

• f(n) = 3(2)ⁿ

• f(n) = 2(3)ⁿ

• f(n) = 6(3)ⁿ

• f(n) = 3(6)ⁿ

Answer explanation

Final answer will look like:

f(n) = a₀(b)ⁿ

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Step 1: Find "b"

Divide a_n values backwards

I will pick last two numbers

b = 486 / 162 = 3

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Step 2: Find "a₀"

Work backwards to find f(0)

f(0) = f(1) / (d)

f(0) = (6) / (3) = 2

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f(n) = 2(3)ⁿ

Sequences can be represented as lists, tables, graphs, or drawings.

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Which two functions represent the sequence?

(hint: the pattern is exponential)

• f(n) = 3(2)ⁿ

• f(n) = 2(3)ⁿ

• f(n) = 6(3)^n-1

• f(n) = 3(6)^n-1

Answer explanation

Final answer will look like:

f(n) = a₀(b)ⁿ

f(n) = a₁(b)^n-1

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We already found one answer

f(n) = a₀(b)ⁿ

f(n) = 2(3)ⁿ

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Find second answer

f(n) = a₁(b)^n-1

f(n) = 6(3)^n-1

Sequences can be represented as lists, tables, graphs, or drawings.

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The points are on a graph. Which function represents the sequence?

(hint: the pattern is exponential)

• f(n) = (2)ⁿ

• f(n) = (3)ⁿ

• f(n) = (4)ⁿ

• f(n) = (5)ⁿ

Answer explanation

Final answer will look like:

f(n) = a₀(b)ⁿ

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Step 1: Find "b"

Divide sequence values backwards

I will pick last two numbers

b = 125 / 25 = 5

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Step 2: Find "a₀"

Find f(0)

f(0) = 1 = a₀

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f(n) = 1(5)ⁿ