Math, asked by drajamohan510, 7 months ago

find the
sum of the first

25 odd naturalnumbers?​

Answers

Answered by msrajendra9gmail
1

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

Answered by BloomingBud
6

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

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