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Question 10

If the sum of the first 11 terms of an arithmetic progression equals that of the first 19 terms, then what is the sum of the first 30 terms?

Solution
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Sum of the first 11 terms = 11/2 ( 2a+10d) 

Sum of the first 19 terms = 19/2 (2a+18d) 

=> 22a+110d = 38a+342d => 16a = -232d

=> 2a = -232/8 d = -29d

Sum of the first 30 terms = 15(2a+29d) = 0

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