Question

sum of all odd numbers between 150 to 200​

Answer 1

4,375

Step-by-step explanation:

in an A.P 151,153,155..................199

$a=151$              $d=2$                 $an=199$

$an=a+(n-1)d\\199=151+(n-1)2\\199=151+2n-2\\199=149+2n\\50=2n\\n=25\\sn=\frac{n}{2}(a+c)\\sn=\frac{25}{2}(151+199)\\sn=\frac{25}{2}(350)\\sn=4,375$

Answer 2

The sum of all odd numbers between 150 to 200​ is 4375

Step-by-step explanation:

odd numbers between 150 - 200

AP is 151,153,155.....199

here

last term = 199

a= 151

d= 153-151 = 2

therefore

$a_n = a+(n-1)d\\\\199 = 151+(n-1)2\\\\199-151=2n-2\\\\48+2 = 2n \\\\50=2n \\\\n = 25$

there are 25 odd numbers between 150-200

now, sum of all odd numbers between 150 to 200​

$S_n = \frac{n}{2}(2a+(n-1)d)\\\\S_2_5 = \frac{25}{2}(2\times 151 +24 \times 2)\\\\S_2_5 = \frac{25}{2}(302+48)\\\\S_2_5 = \frac{25}{2}\times 350\\\\S_2_5 = 175\times 25\\\\S_2_5 = 4375$

hence , The sum of all odd numbers between 150 to 200​ is 4375

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