Advertisements
Advertisements
प्रश्न
Find the sum of first 'n' even natural numbers.
Advertisements
उत्तर
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
संबंधित प्रश्न
Show that a1, a2,..., an... form an AP where an is defined as below:
an = 3 + 4n
Also, find the sum of the first 15 terms.
Show that the sum of all odd integers between 1 and 1000 which are divisible by 3 is 83667.
In an A.P., the sum of first n terms is `(3n^2)/2 + 13/2 n`. Find its 25th term.
The first term of an A.P. is 5, the last term is 45 and the sum of its terms is 1000. Find the number of terms and the common difference of the A.P.
The fourth term of an A.P. is 11 and the eighth term exceeds twice the fourth term by 5. Find the A.P. and the sum of first 50 terms.
If the pth term of an AP is q and its qth term is p then show that its (p + q)th term is zero
Choose the correct alternative answer for the following question .
15, 10, 5,... In this A.P sum of first 10 terms is...
Find the sum of n terms of the series \[\left( 4 - \frac{1}{n} \right) + \left( 4 - \frac{2}{n} \right) + \left( 4 - \frac{3}{n} \right) + . . . . . . . . . .\]
In an A.P. the first term is 8, nth term is 33 and the sum to first n terms is 123. Find n and d, the common differences.
If the sum of P terms of an A.P. is q and the sum of q terms is p, then the sum of p + q terms will be
If 18th and 11th term of an A.P. are in the ratio 3 : 2, then its 21st and 5th terms are in the ratio
Suppose the angles of a triangle are (a − d), a , (a + d) such that , (a + d) >a > (a − d).
Q.5
Q.10
Find the sum of first 1000 positive integers.
Activity :- Let 1 + 2 + 3 + ........ + 1000
Using formula for the sum of first n terms of an A.P.,
Sn = `square`
S1000 = `square/2 (1 + 1000)`
= 500 × 1001
= `square`
Therefore, Sum of the first 1000 positive integer is `square`
The sum of the first 2n terms of the AP: 2, 5, 8, …. is equal to sum of the first n terms of the AP: 57, 59, 61, … then n is equal to ______.
Find the sum of those integers from 1 to 500 which are multiples of 2 or 5.
[Hint (iii) : These numbers will be : multiples of 2 + multiples of 5 – multiples of 2 as well as of 5]
If sum of first 6 terms of an AP is 36 and that of the first 16 terms is 256, find the sum of first 10 terms.
The ratio of the 11th term to the 18th term of an AP is 2 : 3. Find the ratio of the 5th term to the 21st term, and also the ratio of the sum of the first five terms to the sum of the first 21 terms.
Find the value of a25 – a15 for the AP: 6, 9, 12, 15, ………..
