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Writing the formula for a sequence worksheets Grades 11–12

Write the nth-term formula for arithmetic and geometric sequences.

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

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How to do it

Arithmetic: aₙ = a₁ + (n − 1)d, then simplify. Geometric: aₙ = a₁ · rⁿ⁻¹.

−9,−2,5,12,...→an=7n−16-9, -2, 5, 12, ...\quad \to \quad \text{a}_{n} = 7n - 16
a1=−9,d=7\text{a}_{1} = -9,\quad d = 7
−9+(n−1)(7)=7n−16-9 + (n - 1)(7) = 7n - 16aₙ = a₁ + (n − 1)d; then simplify

Example problems

  1. 15,18,21,24,...→15, 18, 21, 24, ...\quad \to \quad
  2. −1,−4,−16,−64,...→-1, -4, -16, -64, ...\quad \to \quad
  3. 5,−15,45,−135,...→5, -15, 45, -135, ...\quad \to \quad
  4. −1,−2,−4,−8,...→-1, -2, -4, -8, ...\quad \to \quad

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