Find the sum of first 123 even natural numbers.

1.	Find the sum of first 123 even natural numbers.
Answer» The even natural numbers are 2, 4, 6, 8, … 27 The above sequence is an A.P. ∴ a = 2, d = 4 - 2 = 2, n = 123 Now, S_n = n/2 [ 2a + (n - 1)d] ∴ S_n = 123/2 [2(2) + (123 - 1)(2)] = 123/2 [2 (2) + 122 (2)] = 123/2 x 2[2 + 122] = 123 x 124 = 15252 ∴ The sum of first 123 even natural numbers is 15252.

Answer»

The even natural numbers are 2, 4, 6, 8, … 27

The above sequence is an A.P.

∴ a = 2, d = 4 - 2 = 2, n = 123

Now, S_n = n/2 [ 2a + (n - 1)d]

∴ S_n = 123/2 [2(2) + (123 - 1)(2)]

= 123/2 [2 (2) + 122 (2)]

= 123/2 x 2[2 + 122]

= 123 x 124

= 15252

∴ The sum of first 123 even natural numbers is 15252.

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