Question

HEY ❤ GUYS PLEASE HELP
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Find the sum of all odd numbers between 100 and 300.....
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Answer 1

$\fcolorbox{red}{pink}{ \huge{Solution :)}}$

The odd integers between 100 and 300 are 101 , 103 , 105 , ..... , 299

Here ,

First term = 101

Common difference = 2

Last term = 299

We know that , the nth term of an AP is given by

$\sf \large \fbox{a_{n}= a + (n - 1)d}$

Substitute the known values , we get

299 = 101 + (n - 1)2

198 = (n - 1)2

99 = (n - 1)

n = 100

We know that , the sum of first n terms of an AP from end is given by

$\large \sf \fbox{S = \frac{n}{2} (a +l)}$

Substitute the known values , we get

$\sf \hookrightarrow S = \frac{100}{2} (101 + 299) \\ \\ \sf \hookrightarrow S = 50(400) \\ \\ \sf \hookrightarrow S = 2000$

Hence , the sum of all odd integers between 100 and 300 is 2000

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