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Find the next number in the series: 11, 13, 17, 19, 23, ?

Understanding the Problem You are given the number series: \[ 11,\ 13,\ 17,\ 19,\ 23,\ ? \] You selected \(25\) , but the correct answer is \(29\) . The fundamental concept you are missing is this: This is a series of consecutive prime numbers. Given Data Series: \(11, 13, 17, 19, 23, ?\) Options: A. \(25\) B. \(27\) C. \(29\) D. \(31\) What Is a Prime Number? A prime number is a number greater than \(1\) that has only two factors : \(1\) the number itself Examples of prime numbers: \[ 2,\ 3,\ 5,\ 7,\ 11,\ 13,\ 17,\ 19,\ 23,\ 29,\ 31,\dots \] Notice that the given series matches part of this prime-number list. Step-by-Step Solution Step 1: Look at the numbers carefully The series is: \[ 11,\ 13,\ 17,\ 19,\ 23 \] All of these are prime numbers . Step 2: Find the next prime number after \(23\) Let us check the numbers after \(23\): \(24\): not prime, because it is divisible by \(2\) \(25\): not prime, because \(25 = 5 \times 5\) \(26\): not prime, because it is divisible by \(2\) \(27\): not prime, because \(27 = 3 \times 9\) \(28\): not prime, because it is divisible by \(2\) \(29\): prime Step 3: Write the next term So the next number in the series is: \[ 29 \] Why \(25\) Is Wrong You chose \(25\), but: \[ 25 = 5 \times 5 \] So \(25\) is not a prime number . Since the pattern is based on prime numbers, \(25\) cannot be the next term. Another Way to Notice the Pattern You may have tried looking at the differences: \[ 13 - 11 = 2,\quad 17 - 13 = 4,\quad 19 - 17 = 2,\quad 23 - 19 = 4 \] This gives: \[ +2,\ +4,\ +2,\ +4 \] If you continue this pattern, you might think the next step is: \[ 23 + 2 = 25 \] But this is a trap . In number series, the difference pattern is not always the real rule. Here, the deeper rule is that all terms are consecutive prime numbers . So always check: Is it an arithmetic pattern? Is it squares/cubes? Is it odd/even? Is it prime numbers? Solution Approach for Similar Questions Check whether the numbers are: odd/even multiples squares or cubes prime numbers Do not rely only on the difference pattern. Find the simplest and strongest rule that fits all the terms. Final Answer \[ \boxed{29} \] Correct option: C Key Point to Remember The missing concept is: The series contains consecutive prime numbers, not just alternating differences. Given: \[ 11,\ 13,\ 17,\ 19,\ 23 \] Next consecutive prime: \[ 29 \] So the next number is \(29\).

Find the next number in the series: 11, 13, 17, 19, 23, ?

Understanding the Problem You are given the number series: \(11,\ 13,\ 17,\ 19,\ 23,\ ?\) You chose \(25\) , but the correct answer is \(29\) . The fundamental concept you may be missing is this: This series is made of consecutive prime numbers. Given Data Series: \(11,\ 13,\ 17,\ 19,\ 23,\ ?\) Options: A. \(25\) B. \(27\) C. \(29\) D. \(31\) Solution Approach Check whether each number belongs to a special pattern. Let us see the numbers one by one: \(11\) is a prime number \(13\) is a prime number \(17\) is a prime number \(19\) is a prime number \(23\) is a prime number These are not just random numbers. They are prime numbers in order , starting from \(11\). Step-by-Step Solution Step 1: Identify the pattern The numbers are: \(11,\ 13,\ 17,\ 19,\ 23\) All of them are prime numbers. Step 2: Write the next prime number after \(23\) The prime numbers after \(23\) are: \(29,\ 31,\ 37,\dots\) So the next prime after \(23\) is \(29\) . Step 3: Check the wrong option \(25\) \(25\) is not a prime number because: \(25 = 5 \times 5\) So it cannot fit in a series of prime numbers. Why \(29\) Is Correct The sequence is: \(11,\ 13,\ 17,\ 19,\ 23,\ 29\) Thus, the correct answer is: \(29\) So, Option C is correct. What You Were Probably Thinking Many students look at the differences: \(13 - 11 = 2\) \(17 - 13 = 4\) \(19 - 17 = 2\) \(23 - 19 = 4\) This gives the pattern: \(+2,\ +4,\ +2,\ +4\) If you continue that, the next step would be: \(23 + 2 = 25\) That is why \(25\) feels tempting. But in number series questions, the stronger and more standard pattern is often the intended one. Here, the numbers are clearly consecutive primes, so \(29\) is the best answer. Important Concept to Remember Prime numbers are numbers greater than \(1\) that have only two factors: \(1\) and the number itself Examples of prime numbers: \(2,\ 3,\ 5,\ 7,\ 11,\ 13,\ 17,\ 19,\ 23,\ 29,\ 31,\dots\) Non-prime numbers like \(25\) and \(27\) are composite because they can be divided by other numbers: \(25 = 5 \times 5\) \(27 = 3 \times 9\) Quick Exam Tip First, check if the numbers belong to a known set: prime numbers squares cubes multiples Only after that, look at the differences. If two patterns seem possible, choose the more natural and standard one. Final Answer The next number in the series is: \(29\) Correct option: C Key Summary The series contains consecutive prime numbers . \(25\) is wrong because it is not prime . The next prime number after \(23\) is \(29\) . If you want, I can also show you how to quickly spot prime-number series in exams so you do not get trapped by answer choices like \(25\).

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Understanding the Problem You are given the number series: \[ 11,\ 13,\ 17,\ 19,\ 23,\ ? \] You selected \(25\) , but the correct answer is \(29\) . The fundamental concept you are missing is this: This is a series of consecutive prime numbers. Given Data Series: \(11, 13, 17, 19, 23, ?\) Options: A. \(25\) B. \(27\) C…
Understanding the Problem You are given the number series: \(11,\ 13,\ 17,\ 19,\ 23,\ ?\) You chose \(25\) , but the correct answer is \(29\) . The fundamental concept you may be missing is this: This series is made of consecutive prime numbers. Given Data Series: \(11,\ 13,\ 17,\ 19,\ 23,\ ?\) Options: A. \(25\) B. \(…