
The next term of the sequence 3, 5, 7, 11, 13, 17, … will be equal to:
Answer
141k+ views
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
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
Latest Vedantu courses for you
Grade 10 | MAHARASHTRABOARD | SCHOOL | English
Vedantu 10 Maharashtra Pro Lite (2025-26)
School Full course for MAHARASHTRABOARD students
₹33,300 per year
EMI starts from ₹2,775 per month
Recently Updated Pages
Difference Between Mutually Exclusive and Independent Events

Difference Between Area and Volume

JEE Main Participating Colleges 2024 - A Complete List of Top Colleges

JEE Main Maths Paper Pattern 2025 – Marking, Sections & Tips

Sign up for JEE Main 2025 Live Classes - Vedantu

JEE Main 2025 Helpline Numbers - Center Contact, Phone Number, Address

Trending doubts
JEE Main 2025 Session 2: Application Form (Out), Exam Dates (Released), Eligibility, & More

JEE Main Exam Marking Scheme: Detailed Breakdown of Marks and Negative Marking

JEE Main 2025: Derivation of Equation of Trajectory in Physics

Electric Field Due to Uniformly Charged Ring for JEE Main 2025 - Formula and Derivation

Learn About Angle Of Deviation In Prism: JEE Main Physics 2025

Degree of Dissociation and Its Formula With Solved Example for JEE

Other Pages
JEE Advanced Marks vs Ranks 2025: Understanding Category-wise Qualifying Marks and Previous Year Cut-offs

JEE Advanced Weightage 2025 Chapter-Wise for Physics, Maths and Chemistry

NCERT Solutions for Class 11 Maths Chapter 6 Permutations and Combinations

JEE Main 2025: Conversion of Galvanometer Into Ammeter And Voltmeter in Physics

Electron Gain Enthalpy and Electron Affinity for JEE

Electrical Field of Charged Spherical Shell - JEE
