# arithmetic

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If 10 times the 10
th
term of an AP is equal to 15 times its 15
th
term, show that its25
th
term is zero.

• arithmetic -

T10 = a+9d
T15 = a+14d

10(a+9d) = 15(a+14d)
10a + 90d = 15a + 210d
5a = -120d
a = -24d

T25 = a + 24d = -24d + 24d = 0

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