
The formula of the sum of first n natural numbers is . If the sum of first n natural number is 325 then find n.
Answer
541.8k+ views
Hint: In this question, we have a formula of sum of first n natural numbers and we know the sum of first n natural numbers given in question. So, put the value of sum in formula and get value of n after solving the quadratic equation.
Complete step-by-step answer:
We know the natural number form an A.P. and we have the sum of first n natural numbers is S=325.
Now, we apply the formula of sum of first n natural numbers mentioned in the question.
We can see quadratic equations in and solve the quadratic equation by using the Sridharacharya formula.
Now, use
We know the number of terms cannot be negative. So, we take only positive value.
So, the value of n is 25.
Note: Whenever we face such types of problems we use some important points. We can see the formula of sum of first n natural numbers mentioned in the question is the same as the formula of sum of first n terms of A.P. So, put the value of sum in formula then after some calculation we can get the required answer.
Complete step-by-step answer:
We know the natural number form an A.P. and we have the sum of first n natural numbers is S=325.
Now, we apply the formula of sum of first n natural numbers mentioned in the question.
We can see quadratic equations in
Now, use
We know the number of terms cannot be negative. So, we take only positive value.
So, the value of n is 25.
Note: Whenever we face such types of problems we use some important points. We can see the formula of sum of first n natural numbers mentioned in the question is the same as the formula of sum of first n terms of A.P. So, put the value of sum in formula then after some calculation we can get the required answer.
Latest Vedantu courses for you
Grade 8 | CBSE | SCHOOL | English
Vedantu 8 CBSE Pro Course - (2025-26)
School Full course for CBSE students
₹45,300 per year
Recently Updated Pages
Master Class 11 Business Studies: Engaging Questions & Answers for Success

Master Class 11 Economics: Engaging Questions & Answers for Success

Master Class 11 Accountancy: Engaging Questions & Answers for Success

Master Class 11 Computer Science: Engaging Questions & Answers for Success

Master Class 11 Maths: Engaging Questions & Answers for Success

Master Class 11 English: Engaging Questions & Answers for Success

Trending doubts
1 Quintal is equal to a 110 kg b 10 kg c 100kg d 1000 class 11 physics CBSE

How do I get the molar mass of urea class 11 chemistry CBSE

How do I convert ms to kmh Give an example class 11 physics CBSE

Where can free central placentation be seen class 11 biology CBSE

What is the molecular weight of NaOH class 11 chemistry CBSE

What is 1s 2s 2p 3s 3p class 11 chemistry CBSE
