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Question
Find the sum of all odd numbers between 351 and 373.
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Solution
Odd numbers between 351 and 373 are 353, 355, 357, 359, ....., 371.
The above series is an A.P.
So, a = 353, d = 2 and an = 371
We know, an = a + (n – 1)d
⇒ 371 = 353 + (n – 1)2
⇒ 371 – 353 = (n –1)2
⇒ 18 = (n –1)2
⇒ n – 1 = 9
⇒ n = 10
Now, `S_n = n/2 (a + a_n)`
= `10/2 (353 + 371)`
= 5(724)
= 3620
Hence, the sum of total odd numbers is 3620.
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