Question

Find the sum of first 123 even natural numbers.

Answer 1

2, 4, 6, ..., 2_n are the even natural numbers.

Here, t₁ = a = 2, t₂ = 4, t₃ = 6

First term (a) = 2
Common difference (d) = t₂ − t₁ = 4 − 2 = 2
Number of terms (n) = 123

We know that,

S_n = `n/2[2a + (n − 1)d]`

∴ S₁₂₃ = `123/2 [2 × 2 + (123 − 1) × 2]`

∴ S₁₂₃ = `123/2 [4 + 122 × 2]`

∴ S₁₂₃ = `123/2 [4 + 244]`

∴ S₁₂₃ = `123/2 × 248`

∴ S₁₂₃ = 123 × 124

∴ S₁₂₃ = 15252

Hence, the sum of first 123 even natural numbers is 15252.