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Question

The sum of the 5th and the 9th terms of an AP is 30. If its 25th term is three times its 8th term, find the common difference of AP.

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Solution

Given t5+t9=30.........(1)

and t25=3t8..............(2)

Solving equation (1),

a+(51)d+a+(91)d=30

a+6d=15........(3)
Now solving equation (2),

a+(251)d=3[a+(81)d]

2a3d=0.........(4)
Multiplying equation (4) by 2, we get 4a6d=0......(5)

On solving equations (3) and (5) simultaneously we get a=3

Substituting a=3 in equation (4)

2(3)3d=0

d=2

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