what is the missing number in the following sequence:
37,41,43,____ ,53,59,61
To find the missing number in the sequence, we need to identify the pattern or rule governing the numbers in the sequence and apply that rule to find the missing term.
Looking at the given sequence: 37, 41, 43, ____, 53, 59, 61
We can observe that the sequence is a list of prime numbers.
Prime numbers are numbers greater than 1 that can only be divided by 1 and themselves without leaving any remainder.
Now let's analyze the sequence:
37 is a prime number.
41 is a prime number.
43 is a prime number.
____ is a missing number.
53 is a prime number.
59 is a prime number.
61 is a prime number.
From the given sequence, we can see that the missing number is also a prime number. By identifying the missing prime number between 43 and 53, we can find the answer.
Starting from 43, let's check each subsequent number if it is a prime number:
43 is prime.
44 is not prime as it is divisible by 2.
45 is not prime as it is divisible by 3.
46 is not prime as it is divisible by 2.
47 is prime.
48 is not prime as it is divisible by 2.
49 is not prime as it is divisible by 7.
50 is not prime as it is divisible by 2.
51 is not prime as it is divisible by 3.
52 is not prime as it is divisible by 2.
Therefore, the missing prime number in the sequence is 47. So the complete sequence is:
37, 41, 43, 47, 53, 59, 61