Summing Geometric Progressions

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? $$a + ar + ar^2 + ar^3 + ...$$