Share
Solving Number Sequence Word Problems: Geometric Progression
Published on May 13, 2026
Word-Problem
Learn to solve word problems involving number sequences by identifying the geometric pattern and calculating the next term. This problem features a geometric progression with a common ratio of 3.
Question
Answer
The problem describes a sequence of buttons placed in boxes.
The number of buttons in each box is as follows:
Box 1: 2 buttons
Box 2: 6 buttons
Box 3: 18 buttons
Box 4: 54 buttons
The number of buttons in each box is as follows:
Box 1: 2 buttons
Box 2: 6 buttons
Box 3: 18 buttons
Box 4: 54 buttons
We need to find the pattern in this sequence. Let’s look at the ratio between consecutive terms:
Ratio of Box 2 to Box 1 =
Ratio of Box 3 to Box 2 =
Ratio of Box 4 to Box 3 =
Ratio of Box 2 to Box 1 =
Ratio of Box 3 to Box 2 =
Ratio of Box 4 to Box 3 =
The pattern is that each term is obtained by multiplying the previous term by 3. This is a geometric sequence with the first term
The formula for the
We need to find the number of buttons in the fifth box, which is the 5th term (
Using the formula:
Using the formula:
Alternatively, we can continue the pattern by multiplying the number of buttons in the fourth box by 3:
Number of buttons in Box 5 = Number of buttons in Box 4 * 3
Number of buttons in Box 5 =
Number of buttons in Box 5 =
Number of buttons in Box 5 = Number of buttons in Box 4 * 3
Number of buttons in Box 5 =
Number of buttons in Box 5 =
The final answer is