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Lesson: Monotonic Sequences

Worksheet • 15 Questions

Q1:

Is the sequence 𝑇 = ο€Ό βˆ’ 1 4  𝑛 𝑛 + 6 increasing, decreasing, or neither?

  • A 𝑇 𝑛 is decreasing.
  • B 𝑇 𝑛 is neither increasing nor decreasing.
  • C 𝑇 𝑛 is increasing.

Q2:

The 𝑛 t h term of a sequence is 𝑇 𝑛 . If 𝑇 = 𝑛 𝑛 2 , is 𝑇 > 𝑇 𝑛 + 1 𝑛 ?

  • Ano
  • Byes

Q3:

Use < , = , or > to complete the following: A sequence with 𝑛 t h term 𝑇 𝑛 is constant if 𝑇 𝑇 𝑛 + 1 𝑛 for each 𝑛 β‰₯ 1 .

  • A >
  • B =
  • C <

Q4:

Use < , = , or > to complete the following: A sequence with 𝑛 t h term 𝑇 𝑛 is strictly increasing if 𝑇 𝑇 𝑛 + 1 𝑛 for each 𝑛 β‰₯ 1 .

  • A =
  • B >
  • C <

Q5:

Is the sequence 𝑇 = βˆ’ 2 3 𝑛 + 1 9 𝑛 increasing, decreasing, or neither?

  • A 𝑇 𝑛 is increasing.
  • B 𝑇 𝑛 is decreasing.
  • C 𝑇 𝑛 is neither increasing nor decreasing.

Q6:

Is the sequence 𝑇 = 2 8 ο€Ό 2 9 2 8  𝑛 𝑛 βˆ’ 2 3 , where 𝑛 β‰₯ 1 increasing, decreasing, or neither?

  • A 𝑇 𝑛 is decreasing.
  • B 𝑇 𝑛 is increasing.
  • C 𝑇 𝑛 is neither increasing nor decreasing.

Q7:

Is the sequence 𝑇 = 1 1 𝑛 + 4 4 𝑛 2 increasing, decreasing, or neither?

  • Aneither increasing nor decreasing
  • Bincreasing
  • Cdecreasing

Q8:

Is the sequence 𝑇 = βˆ’ 9 𝑛 βˆ’ 3 2 𝑛 increasing, decreasing, or neither?

  • Adecreasing
  • Bincreasing
  • Cneither increasing nor decreasing

Q9:

Is the sequence 𝑇 = ( βˆ’ 3 1 ) 𝑛 𝑛 increasing, decreasing or neither?

  • Aincreasing
  • Bneither increasing nor decreasing
  • Cdecreasing

Q10:

Is the sequence 𝑇 = 1 1 9 𝑛 βˆ’ 1 6 𝑛 increasing, decreasing, or neither?

  • Aincreasing
  • Bdecreasing
  • Cneither increasing nor decreasing

Q11:

The 𝑛 t h term of a sequence is 𝑇 𝑛 . If 𝑇 = 𝑛 𝑛 2 , is 𝑇 > 𝑇 𝑛 𝑛 + 1 ?

  • Ayes
  • Bno

Q12:

Is the sequence 𝑇 = βˆ’ 1 1 + 2 𝑛 𝑛 increasing, decreasing, or neither?

  • A 𝑇 𝑛 is decreasing.
  • B 𝑇 𝑛 is increasing.
  • C 𝑇 𝑛 is neither increasing nor decreasing.

Q13:

Use < , = , or > to complete the following: A sequence with 𝑛 t h term 𝑇 𝑛 is strictly decreasing if 𝑇 𝑇 𝑛 + 1 𝑛 for each 𝑛 β‰₯ 1 .

  • A >
  • B <
  • C =

Q14:

A geometric sequence has first term π‘Ž and common ratio π‘Ÿ . In which of the following cases will the sequence be decreasing?

  • A π‘Ž > 0 , 0 < π‘Ÿ < 1
  • B π‘Ž > 1 , βˆ’ 1 < π‘Ÿ < 0
  • C π‘Ž > 0 , βˆ’ 1 < π‘Ÿ < 0
  • D π‘Ž < 0 , 0 < π‘Ÿ < 1
  • E π‘Ž < 0 , βˆ’ 1 < π‘Ÿ < 0

Q15:

Consider the sequence for .

Is ?

  • Ayes
  • Bno

Is ?

  • Ano
  • Byes

Define and by and . Write in simplified form.

  • A
  • B
  • C
  • D
  • E

Using the above and the quadratic formula, find the smallest integer so that whenever .

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