Question

The next term of the sequence 3, 5, 7, 11, 13, 17, … will be equal to:

Answer 1

Hint: Here we had to only find the common thing in each number like whether they all are odd numbers, even numbers, prime numbers or composite numbers. After that we will get the next number easily.

Complete step-by-step answer:

As, we know that the difference of each of the consecutive numbers is not the same as 5 – 3 = 2 but 11 – 7 = 4. So, the sequence cannot be AP.
And as we know that odd numbers are those numbers which are not exactly divisible by 2 or we can say that they give us a remainder equal to 1 when they are divided by 2.
Like 1, 3, 5, 7 are some odd numbers.
So, we can see that the given sequence has all numbers odd.
Now, some odd numbers in between the sequences are missing. Like 9 is odd but it is not present in the given sequence. So, the sequence does not have only an odd number. There should also be another similarity in the number of the sequence.
Now we know that the prime numbers are those numbers which are divisible by only two numbers, first is one and the other one is the number itself.
Like 2, 3, 5, 7, 11 etc are some of the prime numbers.
Now we know that the 2 is the only prime number which is even because other even numbers are also divisible by 2. Which violates the condition of the prime number (divisible by 1 and the number itself).
So, now we can see that the given sequence has all prime numbers in increasing order. But 2 is not present.
So, we can say that the given sequence is the sequence of odd prime numbers.
So, as we know that the next odd prime number after 17 is 19.
Hence, the next number of the given sequence is 19.

Note: Whenever we come up with this type of problem then we should first, check whether the difference of the two consecutive numbers are the same and if it is the same as the numbers are in AP. So, we will apply the formula of AP to find the next term i.e last term + difference of any two consecutive terms of the sequence. And if they are not in AP then we can check whether they are in GP by comparing the ratio of two consecutive terms. And if they are in GP then we will get the next term of the sequence by the formula to find the next term of the GP i.e. product of last term and the ratio of any two consecutive terms. And if the sequence is not of GP then we check whether all of the numbers of the sequence are of the same type and none of that type of number is missing in between. Like we check whether they all are even, odd, prime or composite numbers. By this way we will easily get the required next term of the sequence