find the
sum of the first
25 odd naturalnumbers?
Answers
Answer:
the correct answer is 325.
Step-by-step explanation:
1+2+3+4+5+6+7+8+9+10+11+12+13+14+115+16+17+18+19+20+21+22+23+24+25
9+1=10
2+8=10
3+7=10
4+6=10
5+15=20
11+19=30
12+18=30
13+17=30
14+16=30
10+20=30
21+22+23+24+25=115
115+10×4+20+30×5
115+40+20+150
115+210
325
Odd numbers:
The numbers which are not divisible by 2
The natural odd numbers are
1, 3, 5, 7,........
So it is like an AP
The first term of AP = a = 1
The common difference = d
- Second term - first term = 3 - 1 = 2
Now,
To find:
The sum of the first 25 odd natural numbers,
Now,
The formula to find the sum of the nth term of an AP is
- Sₙ = ⁿ/₂ [2a + (n-1)d]
So,
S₂₅ = ²⁵/₂ [2(1) + (25 - 1)(2)]
S₂₅ = ²⁵/₂ [2 + (24) * (2)]
S₂₅ = ²⁵/₂ [2 + 48]
S₂₅ = 25/2 * 50
S₂₅ = 25 * 25
[As 50/2 = 25]
S₂₅ = 625
Hence,
The sum of the first 25 odd natural numbers is 625.
- - - - -
Another method
The formula to find the sum of the nth term of an AP is (When the last term (l) is given)
- Sₙ = ⁿ/₂ [a + l]
Last 25th term of AP
a₂₅ = a + (n-1)d
a₂₅ = 1 + (25-1)2
a₂₅ = 1 + (24) * 2
a₂₅ = 1 + 48
a₂₅ = 49
Now,
- Sₙ = ⁿ/₂ [a + l]
S₂₅ = 25/2 * [1 + 49]
S₂₅ = 25/2 * 50
S₂₅ = 25 * 25
S₂₅ = 625