Question

Find the sum of all odd numbers between 100 and 200.
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Answer 1

Answer:

The sum of all odd numbers between 100 and 200 is 7500

Step-by-step explanation:

1st odd number after 100 = 101

2nd odd number after 100 = 103

Last odd number between 100 and 200 = 199

a1,a2...an

101,103.....199

an = 199

a1= 101

a2 = 103

Common Difference (d) = 103 - 101

Common Difference (d) = 2

an= a + (n - 1)d

199 = 101 + (n - 1)2

199 - 101 = 2n - 2

98 + 2 = 2n

100 = 2n

2n = 100

n = 100/2

n = 50

Sn = n/2 (a1 + an)

Sn = 50/2 (101 + 199)

Sn = 25 X 300

Sn = 7500

The sum of all odd numbers between 100 and 200 is 7500.

Hope it helps you

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