Question

3. Find the sum of first 25 odd natural
number​

Answer 1

169

Step-by-step explanation:

AP: 1,3,5,..., 25

Given,

a=1, d=2, an= 25

We know that,

an= 1+(n-1)d

=>25-1=(n-1)2

=>n=13

Sn= n/2 {a + an}

=> Sn = 13/2 {1+25}

=> Sn = 13x26/2

=> Sn = 169

Answer 2

Answer:

Sum = 625

Step-by-step explanation:

The series of first 25 odd natural numbers would be like this →

1, 3, 5, 7, 9 ...

Here,

• First term (a) = 1
• Common difference (d) = 3-1 = 2
• Number of terms (n) = 25

Find 25th term of the A.P:

    aₙ = a + (n - 1)d

⇢ a₂₅ = 1 + (25 - 1)2

⇢ a₂₅ = 1 + 24(2)

⇢ a₂₅ = 1 + 48

⇢ a₂₅ = 49

Find sum of 25 terms:

     Sₙ = n/2 (a + aₙ)

⟶ S₂₅ = 25/2 (1 + a₂₅)

⟶ S₂₅ = 25/2 (1 + 49)

⟶ S₂₅ = 25/2 (50)

⟶ S₂₅ = 625

∴ The sum of first 25 odd natural numbers = 625

Short-cut method:

Instead of this method, you can directly apply the Sum of n terms formula and find out the correct answer.

Let's see how !!

Sₙ = n/2 (2a + (n - 1)d)

➝ Sₙ = 25/2 (2 + 24(2))

➝ Sₙ = 25/2 (50)

➝ Sₙ = 25 × 25

➝ Sₙ = 625

In both the methods you arrive at the same answer if solved correctly.