Question

FInd the sum of all odd numbers between 100 and 200.

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Answer 1

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Answer 2

Answer:

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

Step-by-step explanation:

The odd numbers between 100 and 200 are

101, 103, 105, …….199

This series is similar to an arithmetic progression, where

The first number in the series, a = 101

""Common difference d = second term - first term"" = 103 - 101 = 2.

$\bold{t_{n}=a+(n-1) d}$

Here, $t_{n}=199$

199 = 101 + (n-1) 2

199 = 101 + 2n - 2

199 = 99 + 2n

2n = 100

n = 50,  

The number of odd numbers between 100 and 200 are 50.

$\bold{S_{n}=[(2 a+(n-1) d]}$

= [(2(101) + (50-1)2]

= [25(202+98)]

Sn = 7500.