Write and Use Explicit Rules for Arithmetic Sequences

Which formula below shows how to write an EXPLICIT formula for an arithmetic sequence?

• f(n) = f(1) + d(n - 1)

  f(1) = 1st term

  d = common difference

  n = position of a term

  f(n) = value of nth term

• f(n) = d + f(1)(n - 1)

  f(1) = 1st term

  d = common difference

  n = position of a term

  f(n) = value of nth term

• f(1) = d + f(n)(n - 1)

  f(1) = 1st term

  d = common difference

  n = position of a term

  f(n) = value of nth term

Answer explanation

Remember... An explicit rule is:

"First Term Common Difference (n-1) DONE"

Tags

A.12(D) TEKS

Match the following explicit rules to the sequence they each describe:

• 4, 17, 30, 43, ...

• f(n) = -4 - 17(n-1)

• 13, 17, 21, 25, ...

• f(n)= 17 - 4(n-1)

• 17, 13, 9, 5, ...

• f(n)= 13 + 4(n-1)

• -4, -21, -38, -55, ...

• f(n)= 4 + 13(n-1)

Answer explanation

Remember... An explicit rule is:

"First Term Common Difference (n-1) DONE"

Tags

A.12(D) TEKS

Fill in the blanks of the Explicit Rule with the word or expression describing what belongs there:

f(​ (a)   ) = ​​ (b)   + ​ (c)   ​ * (​ (d)   )

• first term
• last term
• common ratio
• common difference
• n - 1
• position # (n)
• n + 1

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A.12(D) TEKS

Organize these sequences into the correct category:

Groups:

(a) ARITHMETIC SEQUENCE

,

(b) NOT ARITHMETIC SEQUENCE

• -1.5, -1, -0.5, 0, ...

• -3, 6, -12, 24, ...

• 3, 5, 9, 15, ...

• 5, 7, 9, 11, ...

• -4, -8, -16, -32, ...

• 2, 4, 8, 16, ...

• 1, 4, 9, 16, ...

• 14, 22, 30, 38, ...

• -10, -7, -4, -1, ...

• -50, -60, -70, -80, ...

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A.12(C) TEKS

Which arithmetic sequence is described by this explicit rule?

a_n = -6 + 8(n - 1)

• -6, 8, 22, 36, ...

• -6, -14, -22, -30, ...

• -6, 2, 10, 18, ...

• 8, 2, -4, -10, ...

Tags

A.12(C) TEKS

Which arithmetic sequence is described by this explicit rule?

a_n = 12 + 4(n - 1)

• 12, 4, -4, -12, ...

• 12, 16, 20, 24, ...

• 4, 16, 28, 40, ...

• answer not here

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A.12(C) TEKS

Which arithmetic sequence is described by this explicit rule?

a_n = -0.5 - 1.5(n - 1)

• -0.5, -2, -3.5, -5, ...

• -1.5, -2, -2.5, -3, ...

• -0.5, 1, 2.5, 4, ...

• answer not here

Tags

A.12(C) TEKS

What is the value of the 99^th term in the sequence described by this explicit rule?

a_n = -0.5 - 1.5(n - 1)

• 52.5

• 148

• -50.5

• -147.5

Tags

A.12(C) TEKS

What is the value of the 57^th term in the sequence described by this explicit rule?

a_n = 13 + 4(n - 1)

• 241

• 237

• 211

• -57

Tags

A.12(C) TEKS

What is the value of the 43^rd term in the sequence below?

(Hint... First write an explicit formula, then use it!)

15, 8, 1, -6, ...

• -195

• -237

• -279

• 309

Tags

A.12(C) TEKS