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Perplex
  • Dashboard
Topics
Exponents & LogarithmsRounding & ErrorSequences & SeriesFinancial MathematicsMatricesComplex Numbers
Cartesian plane & linesFunction TheoryModellingTransformations & asymptotes
2D & 3D GeometryVoronoi DiagramsTrig equations & identitiesVectorsGraph Theory
ProbabilityDescriptive StatisticsBivariate StatisticsDistributions & Random VariablesInference & Hypotheses
DifferentiationIntegrationDifferential Equations
Paper 3
Plus
Calculator Skills
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Perplex

Sequences & Series (Lesson 1/7)

Arithmetic Sequences

1 / 20

The diagram to the right shows the first 3 rows of seating in an amphitheater. The rows are arranged in rings around a central stage.


How many seats are there in the

  • first row?

  • second row?

  • third row?


How many seats will there be in the ​9th​ row?

In the example above, we see that the number of seats in each row is

​
15,21,27…
​


We call this a sequence, which simply means a list of numbers in a specific order. Most interesting sequences follow a pattern, for example:


​
1+4​5+4​9+4​13+4​⋯
​


​
3×3​9×3​27×3​81×3​⋯
​


​
1,11+1​21+2​32+3​53+5​85+8​13⋯
​

Sequences & Series (Lesson 1/7)

Arithmetic Sequences

1 / 20

The diagram to the right shows the first 3 rows of seating in an amphitheater. The rows are arranged in rings around a central stage.


How many seats are there in the

  • first row?

  • second row?

  • third row?


How many seats will there be in the ​9th​ row?

In the example above, we see that the number of seats in each row is

​
15,21,27…
​


We call this a sequence, which simply means a list of numbers in a specific order. Most interesting sequences follow a pattern, for example:


​
1+4​5+4​9+4​13+4​⋯
​


​
3×3​9×3​27×3​81×3​⋯
​


​
1,11+1​21+2​32+3​53+5​85+8​13⋯
​