A geometric sequence is a sequence of numbers where each term is found by multiplying the previous term by a constant ratio. These sequences appear often in math problems involving growth, decay, finance, and patterns.

We’ll explore common types of geometric sequence problems and walk through their step-by-step solutions to help you understand the concepts and apply them with confidence.

1

The second term of a geometric sequence is , and the fifth term is . Determine the sequence.

Solution

The second term of a geometric sequence is , and the fifth term is . Determine the sequence.

3, 6, 12, 24, 48, ...

2

The 1st term of a geometric sequence is and the eighth term is . Find the common ratio, the sum, and the product of the first terms.

Solution

The 1st term of a geometric sequence is and the eighth term is .

Find the common ratio, the sum, and the product of the first terms.

3

Compute the sum of the first terms of the sequence:

Solution

Compute the sum of the first 5 terms of the sequence:

4

Calculate the sum of the terms of the following geometric sequence:

Solution

Calculate the sum of the terms of the following geometric sequence:

5

Calculate the product of the first 5 terms of the sequence:

Solution

6

John has purchased books. The 1st book costs 1 dollar, the 2nd, 2 dollars, the 3rd, 4 dollars, and the 4th, 8 dollars, and so on. How much did John pay for the 20 books?

Solution

John has purchased books. The 1st book costs 1 dollar, the 2nd, 2 dollars, the 3rd, 4 dollars, and the 4th, 8 dollars, and so on. How much did John pay for the 20 books?

dollars

7

The sides of a square, l, have lines drawn between them connecting adjoining sides with their midpoints. This creates another square within the original and this process is continued indefinitely. Calculate the sum of the areas of the infinite squares.

Solution

The sides of a square, l, have lines drawn between them connecting adjoining sides with their midpoints. This creates another square within the original, and this process is continued indefinitely. Calculate the sum of the areas of the infinite squares.

geometric diagram

8

Calculate the fraction that is equivalent to

Solution



9

Calculate the fraction that is equivalent to

Solution



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Emma

Emma

I am passionate about travelling and currently live and work in Paris. I like to spend my time reading, gardening, running, learning languages and exploring new places.