.(ii) Find the common difference of an AP whose first term is 5
and the sum of the first four terms is half the sum of the next
four terms.
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Let d is common difference of AP
Now first 4 terms are 5, 5+d, 5+2d, 5+3d
and next 4 terms 5+4d, 5+5d, 5+6d, 5+7d
Given that, the sum of its first four terms is half the sum of the next four terms.
i.e.,
5 + 5+d + 5+2d + 5+3d=
2
5+4d + 5+5d + 5+6d + 5+7d
20+6d=
2
(20+22d)
20+6d=10+11d
d=2
Hence, the common difference of the given A.P. is 2
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