Question

Plz answer me fast i will mark first clear and complete answer as brainlist. Thank You......
​

Answer 1

Step-by-step explanation:

Note: Sum of n terms Sn = a + (n - 1) * d

(i)

Given: S₁ = a₂ + a₄ + a₆ + ... upto 100 terms.

⇒ S₁ = (100/2)[2a₂ + (100 - 1) * d]

        = 50[2(a + d) + 99d]

        = 50[2a + 2d + 99d]

        = 50[2a + 101d]

        = 100a + 5050d

Then,

a = (S₁ - 5050d)/100

(ii)

Given: S₂ = a₁ + a₃ + a₅+... upto 100 terms.

⇒ S₂ = (100/2)[2a₁ + (100 - 1) * d]

        = 50[2a + 99d]

        = 100a + 4950d

Then,

a = (S₂ - 4950d)/100

On solving (i) & (ii), we get

⇒ (S₁ - 5050d)/100 = (S₂ - 4950d)/100

⇒ (S₁ - 5050d) = (S₂ - 4950d)

⇒ S₁ - 5050d = S₂ - 4950d

⇒ S₁ - S₂ = -4950d + 5050d

⇒ S₁ - S₂ = 100d

⇒ S₁ - S₂/100 = d

Hope it helps!

Answer 2

Step-by-step explanation:

The answer is explained