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Question
Find the sum of all odd numbers between 351 and 373.
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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