Home | Number Concept | Ratio | Recommended Investigations | Geometric Sequences

Geometric Sequences and Series

Consider the geometric sequence: 1, 1/2, 1/4, 1/8, 1/16, . . . What is the ratio between successive terms? Find the sum of the first two numbers in the sequence. Now find the sum of the first three numbers. Continue finding the sums in this manner. What happens to the sum of these numbers?

Consider the geometric sequence: 1, 3/2, 9/4, 27/8, 81/16, . . . What is the ratio between successive terms? Find the sums as you did above. What happens to the sum of these numbers?

Compare the sums of the two series above.

Construct your own geometric sequences. What do you predict will happen to their sums?

 Related External Resources

Does more wins mean more fans at the ballpark?
Determine an attendance-to-win ratio for each of the 28 major league teams and then study the results to see if winning always leads to good attendance.

Ratios, Mars, and the Internet
A lesson plan in which students are involved in calculating real ratios that exist between the planets Earth and Mars.

Using variables and ratios to get you in the right gear
Determine the gear ratios and gears for a 12-speed bicycle.

Submit your idea for an investigation to InterMath.