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Find the sum of the first 20 odd natural numbers by AP method.

Find the sum of the first 20 odd natural numbers by AP method. Find the answer to this question and access a vast question bank that is customised for students.

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Answer:

The odd numbers do not include zero, so the odd first 20 odd numbers would be 1, 3, 5, 7, 9, 11, 13, 15, 17, 19, 21, 23, 25, 27, 29, 31, 33, 35, 37, and 39.

This forms an AP series.

The formula of sum of an A.P series is:

S = n/2[2a + (n − 1) × d]

Where a = Starting term of series d = difference between two consecutive terms (Common difference), and n = Ending term of series.

In above series,

a = 1

d = 2

n = 20

S = 20/2 [2 × 1 + (20 – 1) 2]

S = 10[2 + 38]

S = 400

Hence, the sum of the first 20 odd natural numbers is 400