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Lesson: Introduction to Arithmetic Sequences

Sample Question Videos

Worksheet • 15 Questions • 6 Videos

Q1:

Write the next three terms of the arithmetic sequence 1 5 . 8 , 1 4 . 6 , 1 3 . 4 , 1 2 . 2 , … .

  • A 1 1 , 9 . 8 , 8 . 6
  • B 9 . 8 , 8 . 6 , 7 . 2
  • C 1 1 , 8 . 6 , 7 . 4
  • D 9 . 8 , 8 . 6 , 7 . 4
  • E 1 1 , 9 . 8 , 7 . 4

Q2:

Using the table, determine the expression that represents the value of each term as a function of its position. Then, find the value of the fifteenth term in the sequence.

Position 2 3 4 5 𝑛
Value of Term 4 9 14 19
  • A 5 𝑛 βˆ’ 6 , 69
  • B 𝑛 + 6 , 22
  • C 5 𝑛 + 6 , 81
  • D 6 𝑛 , 10
  • E 5 𝑛 , 75

Q3:

Write the next three terms of the arithmetic sequence 1 6 1 , 1 5 2 , 1 4 3 , 1 3 4 , … .

  • A 1 2 5 , 1 1 6 , 1 0 7
  • B 1 1 6 , 9 8 , 8 0
  • C 1 2 5 , 1 2 3 , 1 2 2
  • D 1 1 6 , 1 0 7 , 9 8
  • E 1 2 5 , 1 1 6 , 9 8

Q4:

Write the next three terms of the arithmetic sequence 3 . 3 , 4 . 2 , 5 . 1 , 6 , … .

  • A 6 . 9 , 7 . 8 , 8 . 7
  • B 7 . 8 , 8 . 7 , 1 1 . 5
  • C 6 . 9 , 8 . 7 , 9 . 6
  • D 7 . 8 , 8 . 7 , 9 . 6
  • E 6 . 9 , 7 . 8 , 9 . 6

Q5:

Find 𝑛 , given 𝑇 = 4 𝑛 + 5 𝑛 and 𝑇 = 2 3 7 𝑛 .

Q6:

Find the first five terms of the sequence whose general term is given by 𝑇 = 4 𝑛 + 1 𝑛 where 𝑛 β‰₯ 1 .

  • A ( 5 , 9 , 1 3 , 1 7 , 2 1 )
  • B ( 5 , 1 4 , 1 9 , 2 4 , 2 9 )
  • C ( 1 , 5 , 9 , 1 3 , 1 7 )
  • D ( 1 , 5 , 9 , 1 3 , 2 1 )
  • E ( 5 , 9 , 1 3 , 2 1 , 2 5 )

Q7:

Write the next three terms of the following sequence: 3 1 , 5 7 , 8 3 , 1 0 9 , … .

  • A 1 3 5 , 1 6 1 , 1 8 7
  • B 1 6 1 , 1 8 8 , 2 1 4
  • C 1 3 5 , 1 3 7 , 1 3 8
  • D 1 6 1 , 1 8 7 , 2 1 3
  • E 1 3 5 , 1 6 1 , 2 1 3

Q8:

If the multiples of any number are written in increasing order, do they form an arithmetic sequence?

  • Ano
  • Byes

Q9:

Given that the sequence π‘Ž , π‘Ž , π‘Ž , π‘Ž , … , 1 2 3 4 is arithmetic, which of the following statements is true?

  • A π‘Ž π‘Ž ( 𝑛 + 1 ) 𝑛 is constant
  • B π‘Ž βˆ’ π‘Ž ( 𝑛 + 1 ) 𝑛 is constant

Q10:

The ending balances in Yara’s savings account for each of the past four years form the sequence 800, 850, 900, 950. Is the sequence arithmetic?

  • Ano
  • Byes

Q11:

Determine the 81st term in the arithmetic sequence which starts 5 1 , 1 0 2 , 1 5 3 , 2 0 4 , … .

Q12:

Use words and symbols to describe the value of each term as a function of its position. Then, find the value of the eighteenth term in the sequence.

Position 13 14 15 16 𝑛
Value of Term 26 28 30 32 ?
  • Amultiply 2, 2 𝑛 , 36
  • Badd 11, 𝑛 + 1 5 , 32
  • Csubtract 2, 𝑛 βˆ’ 2 , 16
  • Dsubtract 11, 𝑛 βˆ’ 1 1 , 28
  • Eadd 2, 𝑛 + 2 , 20

Q13:

Create a five-term sequence by starting with the number 67 and subtracting 8 from each term.

  • A 6 7 , 5 9 , 5 1 , 4 3 , 3 5
  • B 6 7 , 4 3 , 3 5 , 2 7 , 1 9
  • C 5 9 , 5 1 , 4 3 , 3 5 , 2 7
  • D 5 9 , 4 3 , 3 5 , 2 7 , 1 9
  • E 6 7 , 5 1 , 4 3 , 3 5 , 2 7

Q14:

The table shows the number of puzzles Yara finished in a number of weeks. If she continues this pace, write an algebraic expression that can be used to determine the total number of puzzles she would finish after any given number of weeks. How many puzzles will Yara have finished after 43 weeks?

Number of Weeks 1 2 3 4
Number of Puzzles 9 18 27 36
  • A 9 𝑛 , 387 puzzles
  • B 9 𝑛 + 9 , 396 puzzles
  • C 9 + 𝑛 , 52 puzzles
  • D 9 + 𝑛 , 387 puzzles
  • E 9 𝑛 , 52 puzzles

Q15:

Which of the following is an arithmetic sequence?

  • A 𝑇 = βˆ’ 9 𝑛 + 1 𝑛
  • B 𝑇 = √ 𝑛 βˆ’ 7 𝑛
  • C 𝑇 = ( βˆ’ 8 ) 𝑛 𝑛
  • D 𝑇 = 𝑛 βˆ’ 1 𝑛 2
  • E 𝑇 = βˆ’ 9 𝑛 βˆ’ 8 𝑛 + 1 𝑛 2
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