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13,25,48,93,182,?, 712

Challenge your mind with this sequence: 13, 25, 48, 93, 182. Crack the code and find the next term.

by Maivizhi A

Updated Mar 06, 2024

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13,25,48,93,182,?, 712

13,25,48,93,182,?, 712 

The missing number is 359.

To find the missing number in the sequence, let's try to identify a pattern:

13 * 2 - 1 = 25
25 * 2 - 2 = 48
48 * 2 - 3 = 93
93 * 2 - 4 = 182

It seems like each number is being doubled and then subtracted by an incrementing number:

182 * 2 - 5 = 359

So, the missing number is 359.

Let's verify this by continuing the pattern:

359 * 2 - 6 = 712

Therefore, the complete sequence is 13, 25, 48, 93, 182, 359, 712.

The differences follow the pattern we identified. So, the missing number is indeed 359.  

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Sequences and Series in Mathematics 

Sequences and series are fundamental concepts in mathematics, particularly in the field of calculus and analysis. They deal with the ordered lists of numbers (sequences) and the sum of the terms of these sequences (series). Here's an overview of both concepts:

  1. Sequences:
    • A sequence is an ordered list of numbers written in a specific order.
    • Each number in the sequence is called a term.
    • A sequence can be finite (having a specific number of terms) or infinite (going on indefinitely).
    • Sequences are often denoted using notation like {a_n} or (a_n), where "a" represents the terms and "n" represents the position in the sequence.
    • Examples of sequences include arithmetic sequences (where each term is obtained by adding a constant difference to the previous term) and geometric sequences (where each term is obtained by multiplying the previous term by a constant ratio).
  2. Series:
    • A series is the sum of the terms of a sequence.
    • If the sequence is finite, the series is a finite sum. If the sequence is infinite, the series may converge to a finite value or diverge to infinity.
    • Series are often denoted using sigma notation, ∑, where the terms of the sequence are added up over a specific range.
    • Examples of series include arithmetic series (the sum of an arithmetic sequence) and geometric series (the sum of a geometric sequence).

Here are some common types of sequences and series:

  • Arithmetic Sequences and Series: Each term is obtained by adding a fixed number to the previous term.
  • Geometric Sequences and Series: Each term is obtained by multiplying the previous term by a fixed number.
  • Harmonic Series: The series formed by adding the reciprocals of the terms of a sequence.
  • Fibonacci Sequence: A sequence where each term is the sum of the two preceding terms.
  • Power Series: A series where each term is a constant times a variable raised to a power.

The study of sequences and series is essential in various areas of mathematics, including calculus, analysis, number theory, and combinatorics. They are used in many applications, such as physics, engineering, finance, and computer science. Understanding their properties, convergence, and behavior is crucial in solving various mathematical problems.

13,25,48,93,182,?, 712 - FAQs

1. What is a sequence in mathematics?

A sequence is an ordered list of numbers written in a specific order, with each number being a term in the sequence.

2. What is a series in mathematics?

A series is the sum of the terms of a sequence, either finite or infinite.

3. Can sequences be finite or infinite?

Yes, sequences can be either finite, meaning they have a specific number of terms, or infinite, continuing indefinitely.

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