Find the common difference of an AP whose first term is5and the sum of its first four terms is half the sum of the next four terms.
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a1st=a=5
a1st+a2nd+a3rd+a4th=1/(a5th+a6th+a7th+a8th)
a+a+d+a+2d+a+3d=1/(a+4d+a+5d+a+6d+a+7d)
4a+6d=1/(4a+22d)
4×5+6d=1/(4×5+22d)
20+6d=1/(20+22d)
(20+22d)(20+6d)=1
400+120d+440d^2+132d=1
440d^2+152d+400=1
440d^2+152d+399=0
a1st+a2nd+a3rd+a4th=1/(a5th+a6th+a7th+a8th)
a+a+d+a+2d+a+3d=1/(a+4d+a+5d+a+6d+a+7d)
4a+6d=1/(4a+22d)
4×5+6d=1/(4×5+22d)
20+6d=1/(20+22d)
(20+22d)(20+6d)=1
400+120d+440d^2+132d=1
440d^2+152d+400=1
440d^2+152d+399=0
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