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Geometric sequences worksheets Grades 11–12

Find terms of geometric sequences with aₙ = a₁ · rⁿ⁻¹.

The front of the free geometric sequences worksheet
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Free · Worked example · 15 problems · Answer key · US Letter

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How to do it

Each term multiplies by the common ratio r. The nth term is a₁ · rⁿ⁻¹.

128,64,32,16,...term 5=8128, 64, 32, 16, ...\quad \text{term }5 = 8
r=64÷128=12r = 64 \div 128 = \dfrac{1}{2}the common ratio
128×(12)4=8128 \times (\dfrac{1}{2})^{4} = 8aₙ = a₁ · rⁿ⁻¹

Example problems

  1. 2,4,8,16,...term 8=2, 4, 8, 16, ...\quad \text{term }8 =
  2. 128,64,32,16,...term 8=128, 64, 32, 16, ...\quad \text{term }8 =
  3. 243,81,27,9,...term 7=243, 81, 27, 9, ...\quad \text{term }7 =
  4. 3,9,27,81,...term 6=3, 9, 27, 81, ...\quad \text{term }6 =

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