Lesson Worksheet: Sigma Notation Mathematics • 10th Grade

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In this worksheet, we will practice expressing a series in sigma notation as well as expanding and evaluating series represented in sigma notation.

Q1:

Expand −2+7𝑟.

  • A−1−98−119−1310−1511
  • B1,98,119,1310,1511
  • C1+98+119+1310+1511
  • D−1,−98,−119,−1310,−1511

Q2:

Evaluate −8𝑟.

  • A−143
  • B−985
  • C−263
  • D−9415

Q3:

Expand and then evaluate 19𝑟.

  • A19×1+19×2+19×4=1,045.
  • B19×1+19×2+19×3+19×4=874.
  • C19×2+19×3+19×4=1,026.
  • D19×1+19×2+19×3+19×4=570.

Q4:

Expand and then evaluate (2−52).

  • A(2−52)=(2+52)+2+52+2+52+2+52=238
  • B(2−52)=(2−52)+2−52+2−52+2−52=−188
  • C(2−52)=2+52+2+52+2+52=184
  • D(2−52)=(2−52)+2−52+2−52+2−52=−178
  • E(2−52)=(2−52)+2−52+2−52=−178

Q5:

Express the series 8+32+72+128+⋯+512 in sigma notation.

  • A8𝑟
  • B8𝑟
  • C8𝑟
  • D∞8𝑟

Q6:

Express the series 26+27+28+29+30+⋯+84 in sigma notation .

  • A𝑟+1
  • B𝑟+26
  • C𝑟
  • D𝑟

Q7:

Express the series 8+98+998+9,998+⋯ in sigma notation to 𝑛 terms.

  • A∞(10−2)
  • B∞9
  • C(10−2)
  • D9
  • E(11−3)

Q8:

Express the series (32×33)+(33×34)+(34×35)+⋯ in sigma notation.

  • A∞(32×𝑟)(33×𝑟)
  • B(𝑟+31)(𝑟+32)
  • C∞(𝑟+31)(𝑟+32)
  • D∞(𝑟+31)+(𝑟+32)

Q9:

Express the series 54×12+54×24+54×36+⋯+54×240 in sigma notation.

  • A648𝑟
  • B648𝑟
  • C∞648𝑟
  • D(𝑟+648)

Q10:

Express the series 26+39+52+⋯+(13𝑛+13) in sigma notation.

  • A()(3𝑟+23)
  • B(3𝑟+23)
  • C(13𝑟+13)
  • D()(13𝑟+13)
  • E(13𝑟+13)

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