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Arithmetic sequences worksheets Grades 11–12

Find terms of arithmetic sequences with aₙ = a₁ + (n − 1)d.

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Free · Worked example · 18 problems · Answer key · US Letter

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How to do it

Each term adds the common difference d. The nth term is a₁ + (n − 1)d.

−3,−8,−13,−18,...term 13=−63-3, -8, -13, -18, ...\quad \text{term }13 = -63
d=−8−(−3)=−5d = -8 - (-3) = -5the common difference
−3+(13−1)(−5)=−63-3 + (13 - 1)(-5) = -63aₙ = a₁ + (n − 1)d

Example problems

  1. 18,24,30,36,...term 28=18, 24, 30, 36, ...\quad \text{term }28 =
  2. −20,−14,−8,−2,...term 48=-20, -14, -8, -2, ...\quad \text{term }48 =
  3. −11,−18,−25,−32,...term 15=-11, -18, -25, -32, ...\quad \text{term }15 =
  4. −8,−2,4,10,...term 17=-8, -2, 4, 10, ...\quad \text{term }17 =

Sequences and series

  1. Arithmetic sequences
  2. Geometric sequences
  3. Writing the formula for a sequence
  4. Sigma notation
  5. Arithmetic series
  6. Geometric series
  7. Infinite geometric series
  8. Combinations (nCk)
  9. The binomial theorem