find the sum of all odd integers between 1 and 1000 which is divisible by 3.

Hi!
Here is the answer to your question.
 
3, 9, 15, ..., 999 are odd numbers between 1 and 1000 which are divisible by 3.
 
3, 9, 15, …, 999 are in A.P. where a = 3 and d = 6
 
Let 999 be the nth term of A.P.
999 = 3 + (n – 1) × 6
>>  6(n – 1) = 996
>> n – 1 = 166
>> n = 167
Cheers!

  • 14

 x+3...........x999

sn=n/2[2a+(n-1)d]

500*6+99*5

3000+549

3549

  • -4

 a = 3  and d = 2 and l = 999 

an = a +( n - 1 ) d or  3 +( n - 1) 2 = 999 or 2n -2 = 996  2n = 998  or n =499

Hence sn = (499/ 2 )* ( 3 +999 )  =( 499 / 2 ) *1002  = 499 * 501 = 249999

  • -6
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