Find the sum of all odd integers from 1 to 1001.

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Ques: Find the sum of all odd integers from 1 to 1001. 

Ans: The odd integers from 1 to 1001 are 1,3,5,7, ..., 999, 1001.

This is an AP in which a=1, d=(3-1)×2 and I = 1001.

 Let the number of terms be n. Then,

an = 1001

an = a + (n-1) d = 1001 

1 + (n- 1) x 2 = 1001

 n= 501. 

Thus, a=1, l= 1001 and n = 501.

Sn = n(a+l) / 2 = 501(1 + 1001) / 2  = 251001.

 Hence, the required sum is 251001.

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