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Lesson Worksheet: Sequence Formulas Mathematics

In this worksheet, we will practice finding the general term or a recursive formula for a sequence and using them to work out terms in the sequence.

Q1:

Find the first five terms of the sequence whose 𝑛th term is given by 𝑎=𝑛14, where 𝑛1.

  • A(14,13,10,5,2)
  • B(13,10,5,2,11)
  • C(12,10,8,6,4)
  • D(15,18,23,30,39)

Q2:

Find the first five terms of the sequence whose general term is given by 𝑎=𝑛(𝑛34), where 𝑛1.

  • A(33,32,31,30,29)
  • B(33,64,93,120,145)
  • C(33,32,31,30,29)
  • D(33,64,93,120,145)

Q3:

Find the seventh term of the sequence 𝑎=𝑛14.

Q4:

Is the sequence 𝑎=(1)11𝑛22 increasing, decreasing, or neither?

  • A𝑎 is decreasing.
  • B𝑎 is increasing.
  • C𝑎 is neither increasing nor decreasing.

Q5:

Find, in terms of 𝑛, the general term of the sequence coscoscoscos2𝜋,4𝜋,6𝜋,8𝜋,.

  • Acos(2𝑛𝜋)
  • Bcos(2(𝑛+1)𝜋)
  • Ccos(4𝑛𝜋)
  • Dcos(2(𝑛1)𝜋)

Q6:

Find, in terms of 𝑛, the general term of the sequence (18,72,162,288,).

  • A19𝑛1
  • B18𝑛
  • C17𝑛+1
  • D18𝑛
  • E18𝑛

Q7:

Fill in the blank: The 𝑛th term of the sequence 3,92,9, is .

  • A3
  • B3𝑛
  • C3𝑛
  • D31

Q8:

Fill in the blank: The general term of the sequence 3,6,9,12,15, is 𝑎=.

  • A(1)×3𝑛
  • B3𝑛
  • C3𝑛
  • D(1)×3𝑛

Q9:

Fill in the blank: If (𝑎) is a sequence defined as 𝑎=11 and 𝑎=𝑎3, where 𝑛1, then the fourth term equals .

Q10:

Consider the sequence 4,10,22,46,.

Which of the following recursive formulas can be used to calculate successive terms of the sequence for an index 𝑛1?

  • A𝑎=4, 𝑎=52𝑎
  • B𝑎=4, 𝑎=2𝑎
  • C𝑎=4, 𝑎=𝑎+6
  • D𝑎=4, 𝑎=2𝑎+2

This lesson includes 45 additional questions and 333 additional question variations for subscribers.

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