# Find the sum of odd natural numbers from 1 to 101 - Algebra

Sum

Find the sum of odd natural numbers from 1 to 101

#### Solution

The odd natural numbers from 1 to 101 are

1, 3, 5, ....., 101

The above sequence is an A.P.

∴ a = 1, d = 3 – 1 = 2

Let the number of terms in the A.P. be n.

Then, tn = 101

Since tn = a + (n – 1)d,

101 = 1 + (n – 1)(2)

∴ 101 = 1 + 2n – 2

∴ 101 = 2n – 1

∴ 102 = 2n

∴ n = 102/2 = 51

Now, Sn = "n"/2 ("t"_1 + "t"_"n")

∴ S51 = 51/2 (1 + 101)

= 51/2 (102)

= 51 × 51

= 2601

∴ The sum of odd natural numbers from 1 to 101 is 2601.

Concept: Sum of First n Terms of an AP
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