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Summing Geometric Progressions
Age 14 to 18
Challenge Level 
Summing Geometric Progressions printable sheet
Watch the video below to see how Alison works out the sum of the first twenty terms of the sequence: $$2, 8, 32, 128, 512 ...$$
Can you adapt Alison's method to sum the following sequences?
- $3, 9, 27, 81, 243 ...$ up to the 15th term
- $5, 10, 20, 40, 80 ...$ up to the 12th term
- $\sum_{i=1}^{20}(3 \times 2^{i-1})$
- $\frac{1}{2}, \frac{1}{4}, \frac{1}{8}, \frac{1}{16} ...$ up to the 10th term
Can you find an expression for the following sum up to the nth term? $$a + ar + ar^2 + ar^3 + ...$$
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