Find the common difference of an AP whose first term is 5 and the sum of its four terms is half the sum of the next four terms?

Let a and d be the first term and common difference of A.P respectively.

Given, a = 5

Thus, the common difference of A.P. is 2.

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a=5

2*s4 = s8 - s4

2*(4/2 (2a +3d)) = 8/2(2a +7d) - 4/2 (2a +3d)

2*(4a + 6d) = 8a + 28d - 4a - 6d

8a + 12d = 4a + 22d

4a = 10d

d = 2/5 * a

d = 2/5 * 5

d = 2

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