6. The sum of first 13 terms of an ap is 21 and sum of first 21 terms is 13.Find sum of its first 34 terms.
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Step-by-step explanation:
The sum of first 13 terms is 21.
13a+78d=21
The sum of the first 21 terms is 13.
21a+210d=13
multiply the first equation by 21and the second equation by 13.
273a+1638=441
273a+2730d=169
subtract..
1092d=-272
d=-68/273
substitute into 1st equation
13a-136/7=21
a=283/91
hence the sum of the first 34 terms
283*34/91-34*34*33/273
=9622/91-12716/91
=-3094/91
=-34
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