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प्रश्न
If 10 times the 10th term of an AP is equal to 15 times the 15th term, show that its 25th term is zero.
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उत्तर
Let a be the first term and d be the common difference of the AP. Then,
`10 xx a_10 = 15 xx a_15 ` (Given)
⇒10(a +9d) = 15 (a+14d) { an = a+ (n-1)d]
⇒ 2 (a + 9d)=(a +14d)
⇒ 2a + 18d = 3a + 42d
⇒ a= -24d
⇒a + 24d = 0
⇒ a+ (25-1) d=0
⇒ a25 =0
Hence, the 25th term of the AP is 0.
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