Worksheet: Introduction to Sigma Notation

Download Practice

In this worksheet, we will practice expanding an expression written using sigma notation and using it to express the sum of a sequence of terms that follow a rule.

Q1:

Express the series − 1 2 + 1 4 − 1 8 + 1 1 6 − ⋯ in sigma notation .

  • A − 1 2
  • B ∞ 1 2
  • C 1 2
  • D ∞ − 1 2

Q2:

Expand and then evaluate ( 2 − 5 2 ) .

  • A ( 2 − 5 2 ) = ( 2 − 5 2 ) + 2 − 5 2 + 2 − 5 2 = − 1 7 8
  • B ( 2 − 5 2 ) = ( 2 + 5 2 ) + 2 + 5 2 + 2 + 5 2 + 2 + 5 2 = 2 3 8
  • C ( 2 − 5 2 ) = 2 + 5 2 + 2 + 5 2 + 2 + 5 2 = 1 8 4
  • D ( 2 − 5 2 ) = ( 2 − 5 2 ) + 2 − 5 2 + 2 − 5 2 + 2 − 5 2 = − 1 7 8
  • E ( 2 − 5 2 ) = ( 2 − 5 2 ) + 2 − 5 2 + 2 − 5 2 + 2 − 5 2 = − 1 8 8

Q3:

Expand and then evaluate 1 9 𝑟 .

  • A 1 9 × 1 + 1 9 × 2 + 1 9 × 4 = 1 , 0 4 5 .
  • B 1 9 × 1 + 1 9 × 2 + 1 9 × 3 + 1 9 × 4 = 8 7 4 .
  • C 1 9 × 2 + 1 9 × 3 + 1 9 × 4 = 1 , 0 2 6 .
  • D 1 9 × 1 + 1 9 × 2 + 1 9 × 3 + 1 9 × 4 = 5 7 0 .

Q4:

Expand and then evaluate ( 3 1 𝑟 + 8 0 ) .

  • A ( 3 1 × 1 + 8 0 ) + ( 3 1 × 2 + 8 0 ) + ( 3 1 × 3 + 8 0 ) + ( 3 1 × 4 + 8 0 ) = 1 , 1 9 3
  • B ( 3 1 × 1 − 8 0 ) + ( 3 1 × 2 − 8 0 ) + ( 3 1 × 3 − 8 0 ) + ( 3 1 × 4 − 8 0 ) = 3 0 8
  • C ( 3 1 × 1 + 8 0 ) + ( 3 1 × 2 + 8 0 ) + ( 3 1 × 3 + 8 0 ) + ( 3 1 × 4 + 8 0 ) = 1 , 0 5 1
  • D ( 3 1 × 1 + 8 0 ) + ( 3 1 × 2 + 8 0 ) + ( 3 1 × 3 + 8 0 ) + ( 3 1 × 4 + 8 0 ) = 1 , 4 2 8

Q5:

Evaluate 1 4 ( 2 ) .

  • A − 2
  • B 6 3 4
  • C62
  • D126

Q6:

Evaluate − 2 5 .

Q7:

Evaluate − 8 𝑟 .

  • A − 9 8 5
  • B − 1 4 3
  • C − 2 6 3
  • D − 9 4 1 5

Q8:

Evaluate 1 2 .

  • A 1 5 2
  • B − 3 1 3 2
  • C − 1 5 2
  • D 3 1 3 2
  • E 2 9 3 2

Q9:

Express the series ( 3 2 × 3 3 ) + ( 3 3 × 3 4 ) + ( 3 4 × 3 5 ) + ⋯ in sigma notation.

  • A ( 𝑟 + 3 1 ) ( 𝑟 + 3 2 )
  • B ∞ ( 3 2 × 𝑟 ) ( 3 3 × 𝑟 )
  • C ∞ ( 𝑟 + 3 1 ) + ( 𝑟 + 3 2 )
  • D ∞ ( 𝑟 + 3 1 ) ( 𝑟 + 3 2 )

Q10:

Express the series 5 4 × 1 2 + 5 4 × 2 4 + 5 4 × 3 6 + ⋯ + 5 4 × 2 4 0 in sigma notation.

  • A 6 4 8 𝑟
  • B ∞ 6 4 8 𝑟
  • C ( 𝑟 + 6 4 8 )
  • D 6 4 8 𝑟

Q11:

Express the series 8 + 3 2 + 7 2 + 1 2 8 + ⋯ + 5 1 2 in sigma notation.

  • A 8 𝑟
  • B ∞ 8 𝑟
  • C 8 𝑟
  • D 8 𝑟

Q12:

A child wants to build a pyramid using identical wooden cubes. The pyramid’s apex consists of one cube, its second row consists of two cubes, and its third row consists of three cubes, and so on for five rows. Use the sigma notation to describe the amount of cubes needed to build the pyramid and then calculate this number.

  • A 𝑟 , 21 cubes
  • B 𝑟 , 10 cubes
  • C 𝑟 , 10 cubes
  • D 𝑟 , 15 cubes

Q13:

Expand and then evaluate 1 𝑟 + 4 2 − 1 𝑟 + 4 1 .

  • A 1 4 3 − 1 4 2 + 1 4 4 − 1 4 3 + 1 4 5 − 1 4 4 + ⋯ + 1 𝑛 + 4 2 − 1 𝑛 + 4 1 = 𝑛 4 2 ( 𝑛 + 4 2 )
  • B 1 4 3 − 1 4 2 + 1 4 4 − 1 4 3 + 1 4 5 − 1 4 4 + ⋯ + 1 𝑛 + 4 2 − 1 𝑛 + 4 1 = 𝑛 + 8 4 4 2 ( 𝑛 + 4 2 )
  • C 1 4 3 − 1 4 2 + 1 4 4 − 1 4 3 + 1 4 5 − 1 4 4 + ⋯ + 1 𝑛 + 4 2 − 1 𝑛 + 4 1 = 𝑛 − 8 4 4 2 ( 𝑛 + 4 2 )
  • D 1 4 3 − 1 4 2 + 1 4 4 − 1 4 3 + 1 4 5 − 1 4 4 + ⋯ + 1 𝑛 + 4 2 − 1 𝑛 + 4 1 = − 𝑛 4 2 ( 𝑛 + 4 2 )

Q14:

Evaluate ( 2 ) .

  • A 10,560
  • B 12,672
  • C 26,637
  • D 8,064

Q15:

Expand ∞ − 1 5 .

  • A ( 1 5 , 6 2 5 , − 3 , 1 2 5 , 6 2 5 , − 1 2 5 , ⋯ )
  • B ( 1 5 , 6 2 5 − 3 , 1 2 5 + 6 2 5 − 1 2 5 )
  • C ( 1 5 , 6 2 5 , − 3 , 1 2 5 , 6 2 5 , − 1 2 5 )
  • D ( 1 5 , 6 2 5 − 3 , 1 2 5 + 6 2 5 − 1 2 5 + ⋯ )

Q16:

Expand ∞ ( − 1 ) ( 5 6 𝑟 ) .

  • A − 5 6 + 5 6 − 5 6 + 5 6 + ⋯
  • B 3 3 6 − 3 9 2 + 4 4 8 − 5 0 4 + ⋯
  • C 5 6 − 5 6 + 5 6 − 5 6 + ⋯
  • D − 3 3 6 + 3 9 2 − 4 4 8 + 5 0 4 + ⋯

Nagwa uses cookies to ensure you get the best experience on our website. Learn more about our Privacy Policy.