An arithmetic progression has terms. The sum of the odd terms is . The sum of the even terms is . Find the sum of the third term to the eleventh term.
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s ( o d d ) = 2 7 ( a 1 + a 1 3 ) ⟹ 9 8 ( 2 ) = 7 ( a 1 + a 1 3 ) ⟹ a 1 + a 1 3 = 2 8
s ( e v e n ) = 2 6 ( a 2 + a 1 2 ) ⟹ 8 4 = 3 ( a 2 + a 1 2 ) ⟹ a 2 + a 1 2 = 2 8
s = s ( o d d ) + s ( e v e n ) = 9 8 + 8 4 = 1 8 2
The sum of the third term to the eleventh term is 1 8 2 − 2 8 − 2 8 = 1 2 6 .