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प्रश्न
Find the sum of the first n natural numbers.
उत्तर
The first n natural numbers are 1, 2, 3, 4, 5,……..,n
Here, a = 1 and d = (2 – 1) = 1
Sum of n terms of an AP is given by
`s_n = n/2 [2a +(n-1) d]`
`= (n/2) xx [ 2xx1+(n-1) xx1]`
`= (n/2) xx [ 2+n-1] = (n/2) xx (n+1) = (n(n+1))/2`
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संबंधित प्रश्न
In an A.P., if S5 + S7 = 167 and S10=235, then find the A.P., where Sn denotes the sum of its first n terms.
Show that the sum of all odd integers between 1 and 1000 which are divisible by 3 is 83667.
Find the sum of the first 40 positive integers divisible by 3
Determine the A.P. Whose 3rd term is 16 and the 7th term exceeds the 5th term by 12.
If the 8th term of an A.P. is 37 and the 15th term is 15 more than the 12th term, find the A.P. Also, find the sum of first 20 terms of A.P.
First term and the common differences of an A.P. are 6 and 3 respectively; find S27.
Solution: First term = a = 6, common difference = d = 3, S27 = ?
Sn = `"n"/2 [square + ("n" - 1)"d"]` - Formula
Sn = `27/2 [12 + (27 - 1)square]`
= `27/2 xx square`
= 27 × 45
S27 = `square`
If the sum of n terms of an A.P. is 3n2 + 5n then which of its terms is 164?
Q.3
For an A.P., If t1 = 1 and tn = 149 then find Sn.
Activitry :- Here t1= 1, tn = 149, Sn = ?
Sn = `"n"/2 (square + square)`
= `"n"/2 xx square`
= `square` n, where n = 75
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]
