
If the sum of first n even natural numbers is 420, find the value of n.
Answer
532.8k+ views
1 likes
Hint: Here we go through by writing the series of first n even natural numbers as 2,4,6,8,…….n and we saw that this is the series of A.P. so apply the formula of summation of n terms of A.P. to solve our question.
Complete step-by-step answer:
Here in the question it is given that sum of n natural numbers is 420 that means,
2+4+6+8+…….up to n terms=420.
Here we clearly see that the series we write is in the form of A.P. with first term 2 and with a common difference of 2. So we apply the formula of summation of n terms of A.P.
Here first term (a) =2 and common difference (d) =2 and total sum
And we know that summation of n terms of A.P,
Here put the given value in the formula to find out the value of n.
To find the value of n we will solve the above quadratic equation using splitting middle term.
Here n cannot be negative.
Therefore the value of n=20.
Note: Whenever we face such a type of question the key concept for solving the question is first always write the series with some steps and find out from which series it belongs then apply the formula of that series to find out the answer of the question. We should have knowledge about natural numbers as well.
Complete step-by-step answer:
Here in the question it is given that sum of n natural numbers is 420 that means,
2+4+6+8+…….up to n terms=420.
Here we clearly see that the series we write is in the form of A.P. with first term 2 and with a common difference of 2. So we apply the formula of summation of n terms of A.P.
Here first term (a) =2 and common difference (d) =2 and total sum
And we know that summation of n terms of A.P,
Here put the given value in the formula to find out the value of n.
To find the value of n we will solve the above quadratic equation using splitting middle term.
Here n cannot be negative.
Therefore the value of n=20.
Note: Whenever we face such a type of question the key concept for solving the question is first always write the series with some steps and find out from which series it belongs then apply the formula of that series to find out the answer of the question. We should have knowledge about natural numbers as well.
Latest Vedantu courses for you
Grade 11 Science PCM | CBSE | SCHOOL | English
CBSE (2025-26)
School Full course for CBSE students
₹41,848 per year
Recently Updated Pages
Master Class 11 Economics: Engaging Questions & Answers for Success

Master Class 11 Accountancy: Engaging Questions & Answers for Success

Master Class 11 English: Engaging Questions & Answers for Success

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

Master Class 11 Physics: Engaging Questions & Answers for Success

Master Class 11 Biology: Engaging Questions & Answers for Success

Trending doubts
Which one is a true fish A Jellyfish B Starfish C Dogfish class 11 biology CBSE

State and prove Bernoullis theorem class 11 physics CBSE

In which part of the body the blood is purified oxygenation class 11 biology CBSE

1 ton equals to A 100 kg B 1000 kg C 10 kg D 10000 class 11 physics CBSE

Find the value of the expression given below sin 30circ class 11 maths CBSE

Difference Between Prokaryotic Cells and Eukaryotic Cells
