The sum of the first 12 terms and the sum of the first 18 terms of an arithmetic sequence are equal. What is the sum of the first 30 terms?
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Step-by-step explanation:
sum of 11 terms of AP equal the sum of 19 terms of the same AP
S 11 = (11/2)[2a+10d]...(1)
S 19 = (19/2)[2a+18d)...(2)
Equate (1)&(2)
(11/2)[2a+10d]=(19/2)[2a+18d],or
22a+110d=38a+342d,or
16a=232d,or a=-(232/16)d
530=(30/2)[2a+29d]
15[-(464d/16)+29d]
(15/3)[-29 d+29d]
0
The sum of the 30 terms of the AP is 0
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