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. The number 1 appears only once because all primes except for 2 are odd. The rest of the gaps are even numbers.
Given, the series is 2, 3, 5, 7, 11, 13,...... 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 13. We know the prime number after 13 is 17.
2, 3, 5, 7, 11, 13, 17, 19 etc are the prime numbers. Hence, '11' is the correct answer.
The Fibonacci sequence is a series of numbers where a number is the addition of the last two numbers, starting with 0, and 1. The Fibonacci Sequence: 0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55…
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.
If we observe each of the numbers then we can say that every number has only two factors, 1 and the number itself. We know that, if a number is divisible by itself and 1 only then it is called as a prime number. So in the above pattern all numbers are prime numbers.
Detailed Solution
In the series, all numbers are prime numbers. But 9 is an odd number. So, 9 is the odd one out. Hence, the correct answer is "9".
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.
The Fibonacci sequence is a famous group of numbers beginning with 0 and 1 in which each number is the sum of the two before it. It begins 0, 1, 1, 2, 3, 5, 8, 13, 21 and continues infinitely.
2, 3, 5, 8, 12, 17, 23, ____. Therefore, the next number of the given sequence is 30.
2,3,5,7,11,13,17,19,23,29,..... 1 is neither a prime nor a composite number. and 2 is the only prime number which is even. Based on the above numbers the missing number in the series is 17 and 19.
Natural Numbers The numbers that we use when we are counting or ordering {1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11 …}
Prime numbers are numbers that have only 2 factors: 1 and themselves. For example, the first 5 prime numbers are 2, 3, 5, 7, and 11. By contrast, numbers with more than 2 factors are call composite numbers.
twin prime conjecture, also known as Polignac's conjecture, in number theory, assertion that there are infinitely many twin primes, or pairs of primes that differ by 2. For example, 3 and 5, 5 and 7, 11 and 13, and 17 and 19 are twin primes.
Solution: This is a list of prime numbers. The prime number that comes after 17 is 19.
Clearly, the given series consists of prime numbers starting from 2. So, the missing term is the prime number after 11, which is 13.
Fibonacci Numbers (Sequence):
1,1,2,3,5,8,13,21,34,55,89,144,233,377,... Fn=Fn−2+Fn−1 where n≥2 . Each term of the sequence , after the first two, is the sum of the two previous terms. This sequence of numbers was first created by Leonardo Fibonacci in 1202 .
The Fibonacci sequence begins with the following 14 integers: 0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233 ... Each number, starting with the third, adheres to the prescribed formula. For example, the seventh number, 8, is preceded by 3 and 5, which add up to 8.
The next Fibonacci number in the following sequence 1, 1, 2, 3, 5, 8, 13, 21, … is 34.
This is an arithmetic sequence since there is a common difference between each term. In this case, adding 3 to the previous term in the sequence gives the next term. In other words, an=a1+d(n−1) a n = a 1 + d ( n - 1 ) .
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. The number 1 appears only once because all primes except for 2 are odd. The rest of the gaps are even numbers.
The Fibonacci sequence is a type series where each number is the sum of the two that precede it. It starts from 0 and 1 usually. The Fibonacci sequence is given by 0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, and so on. The numbers in the Fibonacci sequence are also called Fibonacci numbers.
There are 11 natural numbers from 2 to 12. They are 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12. There are 5 prime numbers from 2 to 12. They are 2, 3, 5, 7, 11.
Arithmetic Progressions
An arithmetic progression is a sequence where each term is a certain number larger than the previous term. The terms in the sequence are said to increase by a common difference, d. For example: 3, 5, 7, 9, 11, is an arithmetic progression where d = 2.
The series will be, 1,3,5,7,9,11,13,15,17,19,21.