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Geometric series worksheets Grades 11–12

Find the sum of a finite geometric series.

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

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How to do it

Sₙ = a₁(rⁿ − 1) ÷ (r − 1).

the first 5 terms of 3,9,27,...:sum=363\text{the first }5\ \text{terms of }3, 9, 27, ...:\quad \text{sum} = 363
a1=3,r=3,n=5\text{a}_{1} = 3,\quad r = 3,\quad n = 5
3(35−1)3−1=3(243−1)2=363\dfrac{3(3^{5} - 1)}{3 - 1} = \dfrac{3(243 - 1)}{2} = 363Sₙ = a₁(rⁿ − 1) ÷ (r − 1)

Example problems

  1. the first 5 terms of 1,−2,4,...:sum=\text{the first }5\ \text{terms of }1, -2, 4, ...:\quad \text{sum} =
  2. the first 6 terms of 3,6,12,...:sum=\text{the first }6\ \text{terms of }3, 6, 12, ...:\quad \text{sum} =
  3. the first 6 terms of 2,−4,8,...:sum=\text{the first }6\ \text{terms of }2, -4, 8, ...:\quad \text{sum} =
  4. the first 4 terms of 5,15,45,...:sum=\text{the first }4\ \text{terms of }5, 15, 45, ...:\quad \text{sum} =

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