Advertisements
Advertisements
Question
Find the sum of first 'n' even natural numbers.
Advertisements
Solution
First n even natural numbers are 2, 4, 6, 8, ....... 2n
t1 = first term = 2
tn = last term = 2n
Sn = `"n"/2["t"_1 + "t"_"n"]` ......[Formula]
= `"n"/2 [2 + 2"n"]`
= `"n"/2 xx 2(1 + "n")`
= `"n"(1 + "n")`
∴ m of first n even natural numbers is n(1 + n).
APPEARS IN
RELATED QUESTIONS
Find the number of natural numbers between 101 and 999 which are divisible by both 2 and 5.
Find the sum of first 8 multiples of 3
Find the sum of the following arithmetic progressions:
3, 9/2, 6, 15/2, ... to 25 terms
Find the sum of all even integers between 101 and 999.
Find the sum of the first 40 positive integers divisible by 3
How many two-digit number are divisible by 6?
Write the next term for the AP` sqrt( 8), sqrt(18), sqrt(32),.........`
Find the first term and common difference for the following A.P.:
5, 1, –3, –7, ...
Rs 1000 is invested at 10 percent simple interest. Check at the end of every year if the total interest amount is in A.P. If this is an A.P. then find interest amount after 20 years. For this complete the following activity.
For what value of n, the nth terms of the arithmetic progressions 63, 65, 67, ... and 3, 10, 17, ... equal?
The sum of the first 7 terms of an A.P. is 63 and the sum of its next 7 terms is 161. Find the 28th term of this A.P.
The sum of first n terms of an A.P. is 3n2 + 4n. Find the 25th term of this A.P.
The first term of an A.P. is p and its common difference is q. Find its 10th term.
If the nth term of an A.P. is 2n + 1, then the sum of first n terms of the A.P. is
In a Arithmetic Progression (A.P.) the fourth and sixth terms are 8 and 14 respectively. Find that:
(i) first term
(ii) common difference
(iii) sum of the first 20 terms.
Find the sum of the integers between 100 and 200 that are
- divisible by 9
- not divisible by 9
[Hint (ii) : These numbers will be : Total numbers – Total numbers divisible by 9]
In the month of April to June 2022, the exports of passenger cars from India increased by 26% in the corresponding quarter of 2021-22, as per a report. A car manufacturing company planned to produce 1800 cars in 4th year and 2600 cars in 8th year. Assuming that the production increases uniformly by a fixed number every year. |
Based on the above information answer the following questions.
- Find the production in the 1st year
- Find the production in the 12th year.
- Find the total production in first 10 years.
[OR]
In how many years will the total production reach 31200 cars?
Solve the equation:
– 4 + (–1) + 2 + 5 + ... + x = 437
Which term of the Arithmetic Progression (A.P.) 15, 30, 45, 60...... is 300?
Hence find the sum of all the terms of the Arithmetic Progression (A.P.)
The sum of all two digit numbers is ______.
