[Solved] Complete the series choosing the missing number: 2, 3, 5, 7 (2024)

FAQs

[Solved] Complete the series choosing the missing number: 2, 3, 5, 7? ›

Detailed Solution

The primes up to 50 are 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43 and 47. The sequence of gaps—the differences between each prime and the next—is 1, 2, 2, 4, 2, 4, 2, 4, 6, 2, 6, 4, 2 and 4.

Solution: Given, the series is 2, 3, 5, 7, 11, 13, 17, 19,...... From the given series we can observe that the numbers follow a pattern of consecutive prime numbers. So, the missing number in the series will be the next prime number after 19.

The number that comes next in the series 2, 3, 5, 7, 11, 13 would be 17. This is because this is a list of prime numbers. Prime numbers are numbers that are only divisible by themselves and by 1.

Also if we consider any two successive prime numbers from the above sequence then we can observe that all the integers present in between are composite numbers. Also 2 is the smallest prime number. So we can say that the given pattern of numbers: \[2,3,5,7,11,13,17,19,23,29\] will describe the first ten prime numbers.

Detailed Solution

All are consecutive prime number starting from 2. Prime numbers are those number who is divided by one or by itself. 2, 3, 5, 7, 11, 13, 17, 19 etc are the prime numbers. Hence, '11' is the correct answer.

Explanation: The primes, in order, are: 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, ...

Which of the following numbers does not belong in the pattern 2, 3, 5, 7, 11, and 12? 12 is the odd one because the pattern is formed by taking consecutive prime numbers.

Missing numbers are the numbers that got missed in the given series of numbers with similar differences among them. The process of writing the missing numbers is termed as finding similar changes between those numbers and filling their missing values in their specific series and places.

The first differences are: 1, 3, 2, 4, 2, 4, 1, 3, -1 … Finally the sequences is 1, 2, 5, 7, 11, 13, 17, 18, 21, 20, ..

What comes next in the sequence 2, 3, 7, 23? ›

23 is obtained by taking off the comma between 2 and 3, the two first members. Hence, the next after 23 is 37, which is obtained by taking off the comma between the next two members 3 and 7. Answer. The next in the sequence is 37.

3, 5, 7, 11,13, ? The series given above is a prime number series - 3, 5, 7, 11,13, therefore the next number is 17. Hence, '17' is the correct answer.

If you have a series of numbers as follows: 1, 2, 3, 5, 7, what would the next number be? 1, 1, 2, 3, 5, 7, 11, 15, 22, 30, 42, 56, 77, 101, 135, 176, 231, 297, 385, 490, 627, 792, 1002, 1255, 1575, 1958, 2436, 3010, 3718, 4565, 5604, ...

Solution: This is a list of prime numbers. The prime number that comes after 17 is 19.

This is an arithmetic sequence since there is a common difference between each term. In this case, adding 2 to the previous term in the sequence gives the next term.

The sequence that is given to us is 1, 3, 5, 7, 9, ... a₅ - a₄ = 9 - 7 = 2. Hence, from the above simplification we can see that the common difference is 2. Therefore, the general term for the sequence 1, 3, 5, 7, 9, . . . is 2n - 1.

Answer and Explanation:

According to the question, the sequence 2, 3, 5, 6, 7, 10, ... consists of all-natural numbers which are neither perfect squares nor perfect cubes.

The Fibonacci sequence is the series of numbers: 0, 1, 1, 2, 3, 5, 8, 13, 21, 34... In this series, the next number is found by adding the two numbers before it. Hence, the next term in the series is 8 + 13 = 21. Q.

In an arithmetic sequence, the difference between consecutive terms is always the same. For example, the sequence 3, 5, 7, 9 ... is arithmetic because the difference between consecutive terms is always two.