Lesson Worksheet: Representing Sequences Mathematics

In this worksheet, we will practice representing a sequence as a function of a positive integer variable called an index (n).

Q1:

Mrs. Jones has $3,250 in her bank account. If she plans to deposit $100 per month, write the first 6 terms of a sequence that would represent her monthly account balances starting with her current balance as the first term.

  • A3,350,3,450,3,550,3,650,3,750,3,850
  • B3,350,3,550,3,650,3,750,3,850,3,950
  • C3,250,3,350,3,450,3,550,3,650,3,750
  • D3,250,3,550,3,650,3,750,3,850,3,950
  • E3,250,3,450,3,550,3,650,3,750,3,850

Q2:

Which of the following expressions can be used to find the 𝑛th term of the given sequence, where 𝑛 represents the position of a term in the sequence?

Position 1 2 3 4 5
Value of Term58111417
  • A3𝑛+2
  • B𝑛+2
  • C3𝑛
  • D3𝑛+2
  • E𝑛+2

Q3:

Find the first 3 terms of the sequence whose general term 𝑎=𝑛𝑛+1.

  • A0, 12, and 34
  • B12, 23, and 34
  • C0, 12, and 23
  • D12, 23, and 34
  • E0, 23, and 34

Q4:

Find the fourth term in the sequence 1,12,13,.

  • A14
  • B15
  • C13
  • D15
  • E14

Q5:

Which of the following expressions can be used to find the 𝑛th term of the sequence {2,1,6,}?

  • A𝑛2
  • B𝑛3
  • C𝑛
  • D𝑛3
  • E𝑛+3

Q6:

Consider the sequence 12,23,34,45,.

What is the general term of this sequence?

  • A𝑛2
  • B𝑛𝑛+1
  • C1𝑛+1
  • D𝑛𝑛+2
  • E1𝑛

Q7:

In any sequence pattern, if the difference between any two successive terms is a fixed number, 𝑑, then this is an arithmetic sequence.

Consider the sequence 1,4,7,10,, and then answer the following questions.

Is the sequence arithmetic?

  • ANo
  • BYes

What is the value of 𝑑?

What is the general term of this sequence with 𝑛0?

  • A3𝑛1
  • B3𝑛+4
  • C𝑛+1
  • D𝑛1
  • E3𝑛+1

Q8:

In a geometric sequence, the ratio between any two successive terms is a fixed ratio 𝑟.

Consider the sequence 12,14,18,116,.

Is this sequence geometric?

  • ANo
  • BYes

Consider the sequence 12,14,18,116,.

What is the value of 𝑟?

  • A4
  • B18
  • C14
  • D12
  • E2

Consider the sequence 12,14,18,116,.

What is the general term of this sequence?

  • A12, 𝑛1
  • B14, 𝑛1
  • C212, 𝑛1
  • D1212, 𝑛1
  • E1414, 𝑛1

Q9:

Consider the sequence 1,1,34,48,.

Which of the following is the general term of this sequence such that 𝑛0?

  • A𝑛12
  • B2𝑛2
  • C𝑛+12
  • D𝑛2
  • E𝑛+22

Q10:

Consider the sequence 12,25,310,417,.

Which of the following is the general term of this sequence such that 𝑛1?

  • A(1)𝑛𝑛+1
  • B𝑛𝑛+1
  • C(1)𝑛𝑛+1
  • D(1)𝑛𝑛1
  • E(1)𝑛𝑛+1

This lesson includes 15 additional questions and 225 additional question variations for subscribers.

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