A sequence in which the difference between any two consecutive terms is a constant is called as arithmetic progression.
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 nth term of this sequence is 2n + 1 .
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.
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. In other words, an=a1+d(n−1) a n = a 1 + d ( n - 1 ) . This is the formula of an arithmetic sequence.
The series will be, 1,3,5,7,9,11,13,15,17,19,21.
Hence, the sum of 1+3+5+7+9+11+13+15+17 is 81.
Common FAQs about prime numbers
A prime number is a number that can only be divided by itself and 1 without remainders. What are the prime numbers from 1 to 100? The prime numbers from 1 to 100 are: 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97.
Answer: The equation for the nth term of the arithmetic sequence -3, -5, -7, -9, ...... is -2n - 1.
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.
∴nth term is 2n−1. Was this answer helpful?
The given sequence is 1, 3, -5, 7, 9, -11, 13, 15, -17…………. . In the given sequence, the absolute values of the terms are in arithmetic progression with a negative number appearing after every two positive terms of the sequence.
The numbers given in the sequence are prime numbers as they can be divided only by 1 and itself. Hence, the number line series will be 1, 3, 5, 7, 11, 13, 17, and 19. Solution: The missing number found in the following sequence is 35.
Answer and Explanation: The value of 1 + 3 - 5 - 7 + 9 + 11 - 13 - 15 + 17 + ... - 79 + 81 is 1. The first step to finding our answer is to determine the pattern of the sequence.
Let us find the sum of all given numbers. The sum of all the observations = 1+3+5+7+9+11+13 = 49.
Answer: The mean of 1, 3, 5, 7, 9, 11, 13 is 7.
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.
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…
In the sequence 2, 4, 6, 8, 10... there is an obvious pattern. Such sequences can be expressed in terms of the nth term of the sequence. In this case, the nth term = 2n.
The sequence is 5 , 9 , 13 , 17 , ⋯ . As the difference between consecutive terms is equal, the sequence is an arithmetic progression. The first term of the AP is 5 and the common difference is 4. So, the general term of the AP is a n = 5 + 4 ( n − 1 ) .
The next number in the series 3, 9, 5, 15, 11, 33, 29, is 81.
Solution: Given, the arithmetic sequence is 9, 11, 13, 15,.... We have to find the equation for the nth term of the sequence. Therefore, the equation for the nth term of the sequence is an = 2n + 7.
This solution deals with arithmetic sequences. The nth terms: 3,5,7,9,11,13,15,17...
The numbers 7 × 11 × 13 + 13 and 7 × 6 × 5 × 4 × 3 × 2 × 1 + 5 are composite numbers since on simplification the numbers have (2,3,13 and 1) and (5,1009 and 1) as their factors respectively.
Clearly, the given series consists of prime numbers starting from 2. So, the missing term is the prime number after 11, which is 13. Was this answer helpful?
The primes up to 50 are 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43 and 47.