Q. 20 A5.0( 2 Votes )

# Find the sum of all the odd numbers lying between 100 and 200.

The odd numbers lying between 100 and 200 are

101, 103, 105,…, 199

a2 – a1 = 103 – 101 = 2

a3 – a2 = 105 – 103 = 2

a3 – a2 = a2 – a1 = 2

Therefore, the series is in AP

Here, a = 101, d = 2 and an = 199

We know that,

an = a + (n – 1)d

199 = 101 + (n – 1)2

199 – 101 = (n – 1)2

98 = (n – 1)2

49 = (n – 1)

n = 50

Now, we have to find the sum of this AP

S50 = 25[202 + 49 × 2]

S50 = 25[300]

S50 = 7500

Hence, the sum of all odd numbers lying between 100 and 200 is 7500.

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