Worksheet: Writing Arithmetic Series in Sigma Notation

In this worksheet, we will practice using the summation notation to describe an arithmetic series and finding the summation’s value.

Q1:

Represent the series 6 3 + 1 1 2 + 1 6 1 + + 3 0 8 using sigma notation.

  • A ( 4 9 𝑟 + 1 4 )
  • B ( 4 9 𝑟 + 1 4 )
  • C ( 2 7 𝑟 + 3 6 )
  • D ( 4 9 𝑟 + 1 4 )
  • E ( 2 7 𝑟 + 3 6 )

Q2:

Express the series 2 6 + 3 9 + 5 2 + + ( 1 3 𝑛 + 1 3 ) in sigma notation.

  • A ( 1 3 𝑛 + 1 3 ) 𝑟 = 2 6 ( 1 3 𝑟 + 1 3 )
  • B 𝑛 𝑟 = 2 6 ( 1 3 𝑟 + 1 3 )
  • C 𝑛 𝑟 = 1 ( 3 𝑟 + 2 3 )
  • D 𝑛 𝑟 = 1 ( 1 3 𝑟 + 1 3 )
  • E ( 1 3 𝑛 + 1 3 ) 𝑟 = 2 6 ( 3 𝑟 + 2 3 )

Q3:

Find the value of 7 + 9 + 1 1 + + 3 7 1 2 + 1 4 + 1 6 + + 1 7 2 .

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

Q4:

Find the value of ( 6 + 7 + 8 + + 1 4 ) ( 6 + 7 + 8 + + 1 3 ) .

Q5:

Find the value of 1 + 4 + 7 + + 1 3 8 8 + 9 8 + 1 0 8 + + 1 3 8 .

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

Q6:

Express the series 8 + 9 8 + 9 9 8 + 9 9 9 8 + in sigma notation to 𝑛 terms.

  • A 𝑟 = 1 𝑟 ( 1 0 2 )
  • B 𝑛 𝑟 = 1 𝑟 9
  • C 𝑛 𝑟 = 1 𝑟 ( 1 1 3 )
  • D 𝑛 𝑟 = 1 𝑟 ( 1 0 2 )
  • E 𝑟 = 1 𝑟 9

Q7:

Represent the series 2 5 × 2 6 × 2 7 + 2 7 × 2 8 × 2 9 + 2 9 × 3 0 × 3 1 + using sigma notation.

  • A 𝑟 = 2 5 𝑟 ( 𝑟 + 1 ) ( 𝑟 + 2 )
  • B 𝑟 = 1 ( 2 6 𝑟 1 ) ( 2 6 𝑟 ) ( 2 6 𝑟 + 1 )
  • C 1 5 𝑟 = 1 3 ( 2 𝑟 1 ) ( 2 𝑟 ) ( 2 𝑟 + 1 )
  • D 𝑟 = 1 3 ( 2 𝑟 1 ) ( 2 𝑟 ) ( 2 𝑟 + 1 )

Q8:

Express the series 4 9 6 4 9 7 + 4 9 8 4 9 9 + 5 3 1 in sigma notation.

  • A 𝑟 = 1 𝑟 ( 1 ) ( 𝑟 + 4 9 5 )
  • B 𝑟 = 1 𝑟 + 1 ( 1 ) ( 𝑟 + 4 9 5 )
  • C 3 6 𝑟 = 1 𝑟 ( 1 ) ( 𝑟 + 4 9 5 )
  • D 3 6 𝑟 = 1 𝑟 + 1 ( 1 ) ( 𝑟 + 4 9 5 )

Q9:

Express the series 2 6 + 2 7 + 2 8 + 2 9 + 3 0 + + 8 4 in sigma notation .

  • A 𝑟 + 2 6
  • B 𝑟
  • C 𝑟 + 1
  • D 𝑟

Q10:

Express the series 1 2 5 + 2 1 6 + 3 4 3 + + 7 2 9 in sigma notation.

  • A 𝑟 = 5 3 𝑟
  • B 9 𝑟 = 5 3 ( 𝑟 )
  • C 9 𝑟 = 1 3 𝑟
  • D 9 𝑟 = 5 3 𝑟

Q11:

Express the series 1 8 3 + 3 6 6 + 5 4 9 + 7 3 2 + in sigma notation.

  • A 𝑟 = 1 𝑟 + 1 8 2
  • B 𝑟 = 1 𝑟 + 1 8 3
  • C 4 𝑟 = 1 1 8 3 𝑟
  • D 𝑟 = 1 1 8 3 𝑟

Q12:

Express the series 5 2 6 × 2 7 + 5 2 7 × 2 8 + 5 2 8 × 2 9 + 5 2 9 × 3 0 + + 5 3 4 × 3 5 in sigma notation.

  • A 3 5 𝑟 = 2 6 5 𝑟 ( 𝑟 + 1 )
  • B 𝑟 = 2 6 5 𝑟 ( 𝑟 + 1 )
  • C 3 4 𝑟 = 1 5 𝑟 ( 𝑟 + 1 )
  • D 3 4 𝑟 = 2 6 5 𝑟 ( 𝑟 + 1 )

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