# 7, 8, 17, 42, ?, 172, 293

What lies beyond the unknown? Explore the enigma of the missing number in this intriguing numerical sequence.

by Maivizhi A

**Updated **Mar 06, 2024

## 7, 8, 17, 42, ?, 172, 293

The 7, 8, 17, 42, 91, 172, 293

To find the missing number in the sequence, let's analyze the pattern:

7, 8, 17, 42, ?, 172, 293

The pattern seems to be getting more complex with each step. Let's examine the differences between consecutive numbers:

8 - 7 = 1 17 - 8 = 9 42 - 17 = 25

The differences between consecutive numbers seem to be the squares of consecutive odd numbers:

1 = 1^2 9 = 3^2 25 = 5^2

Following this pattern, the next difference would be 7^2 = 49. So, to find the missing number, we can add 49 to 42:

42 + 49 = 91

So, the missing number in the sequence is 91.

The updated sequence is: 7, 8, 17, 42, 91, 172, 293

## Applications of Arithmetic Sequences in Real Life

Arithmetic sequences, which are sequences of numbers in which the difference between any two consecutive terms is constant, have numerous applications in real life across various fields. Here are some examples:

- Finance and Economics:
- Loan Repayment: When you take out a loan with fixed monthly payments, the amount you owe decreases in an arithmetic sequence.
- Depreciation: The decrease in value of an asset over time, such as a car or equipment, often follows an arithmetic sequence.

- Physics and Engineering:
- Uniform Motion: When an object moves at a constant speed, its position over time follows an arithmetic sequence.
- Gravitational Acceleration: The acceleration due to gravity near the Earth's surface causes the velocity of a falling object to increase in an arithmetic sequence.

- Computer Science:
- Memory Allocation: In computer programming, memory addresses are often allocated in arithmetic sequences to optimize access speed.
- Progressions in Algorithms: Some algorithms involve arithmetic sequences, such as loop iterations in iterative algorithms.

- Manufacturing and Production:
- Assembly Line Production: If a certain number of items are produced at regular intervals, the total number of items produced follows an arithmetic sequence.
- Inventory Management: Replenishing inventory at regular intervals can be modeled using arithmetic sequences.

- Telecommunications:
- Data Transmission: The transmission of data packets in networks can follow an arithmetic sequence based on timing protocols.
- Frequency Allocation: In wireless communication systems, the allocation of frequency channels can follow an arithmetic sequence to avoid interference.

- Sports and Games:
- Scoring in Games: In sports such as basketball or soccer, scoring can occur in an arithmetic sequence over time.
- Growth in Sports Records: The progression of records in sports like track and field often follows an arithmetic sequence.

- Construction and Architecture:
- Construction Schedules: The scheduling of construction tasks often follows an arithmetic sequence, especially when tasks have fixed durations.
- Height of Structures: The height of floors in a building or the number of steps in a staircase can follow an arithmetic sequence.

- Education:
- Grade Point Average (GPA): If a student's grades in different courses follow a weighted average, the calculation can be based on an arithmetic sequence.
- Curriculum Planning: Some educational programs are structured with an arithmetic sequence in mind, such as increasing difficulty levels of courses over time.

These are just a few examples, but arithmetic sequences are pervasive in various aspects of daily life and professional fields. Their predictability and regularity make them valuable tools for modeling and analyzing real-world phenomena.

## 7, 8, 17, 42, ?, 172, 293 - FAQs

### 1. What is the missing number in the sequence 7, 8, 17, 42, ?, 172, 293?

The missing number is 91.

### 2. How did you determine the missing number in the sequence?

By observing the pattern of differences between consecutive terms, which follow the squares of consecutive odd numbers.

### 3. What is an arithmetic sequence?

An arithmetic sequence is a sequence of numbers where the difference between any two consecutive terms is constant.

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