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Show that the sum of all odd integers between1to 1000 divisible by 3is 83667

Posted by Kiran Yadav 6 years, 11 months ago

CBSE > Class 10 > Mathematics

1 answers

Navneet Verma 6 years, 11 months ago

A.P : 3,9,15,------------999. Here a= 3, d=6, An = 999. An= a+ (n-1)d 999=3 + ( n-1)6 999=3+ 6n - 6 999 = 6n- 3 999+3=6n 1002=6n 1002/6=n 167=n. Sn = n/2 [2a+(n-1) d ] S167 = 167/2 [2×3+(167-1)×6] = 167/2 [6+166×6] = 167/2 [1002] = 167/2× 1002 =167×501 = 83667. Hence proved

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