Geometric Progression Concepts and Problems

The video tutorial introduces the concept of geometric progression (PG) and explains the formula for the general term. It provides examples to illustrate how to find terms in a PG and discusses real-world applications, such as population growth and viral transmission. The tutorial emphasizes understanding the pattern in PGs and applying the formula to solve problems.

What is the common ratio in the geometric progression 1, 2, 4?

• 1

• 2

• 4

• 3

If the first term of a GP is 3 and the common ratio is 2, what is the second term?

• 3

• 5

• 6

• 9

How do you represent the nth term of a geometric progression?

• a_n = a_1 + r^n

• a_n = a_1 * r^(n-1)

• a_n = a_1 * r^n

• a_n = a_1 + r^(n-1)

In the formula a_n = a_1 * r^(n-1), what does 'a_1' represent?

• The exponent

• The first term

• The common ratio

• The nth term

Using the formula, find the 6th term of the GP: 4, 12, 36.

• 2916

• 108

• 324

• 972

What is the common ratio in the GP: 5/16, 5/8, 5/4?

• 2

• 4

• 1/2

• 8

If a bacteria population doubles every day starting from 40, how many bacteria will there be on the 10th day?

• 10240

• 20480

• 4096

• 2048

In a GP, if the 10th term is 512 and the first term is 1, what is the common ratio?

• 4

• 8

• 2

• 16

Determine the position of the term 160 in the GP: 5/16, 5/8, 5/4.

• 8th

• 10th

• 11th

• 9th

What is the value of 2 raised to the power of 9?

• 2048

• 1024

• 512

• 256