Year 11 · Specialist Mathematics

Geometric sequences and series

Free examples and worked answers. No account needed.

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Practise the method.

Finite sums, convergent infinite sums and ratios.

Example 1

Geometric terms shown as proportional pieces.1234Term numberFirst term 9 · multiply by 2
Select successive terms and follow how doubling builds the series.
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Answer:

Example 2

Geometric terms shown as proportional pieces.Each new piece is half the previous one
More pieces, smaller additionsEach addition is smaller than the last
Add smaller pieces to explore convergence. A finite picture suggests the pattern; justify the infinite sum algebraically.
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Answer:

Example 3

Geometric terms shown as proportional pieces.123456Term numberFirst term 7 · multiply by 2
Select successive terms and follow how doubling builds the series.
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Answer: