Question

If 10 times the 10th term of an ap is equal to 15 times the 15th term show that its 25th term is 0

Answer 1

Answer:

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Answer 2

$\sf{\bold{\green{\underline{\underline{Given}}}}}$

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• 10 times the 10th term of an AP is equal to 15 times the 15th term

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$\sf{\bold{\green{\underline{\underline{To\: Prove}}}}}$

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• 25th term is 0

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$\sf{\bold{\green{\underline{\underline{Solution}}}}}$

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Let the first term of the A.P be a

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Let the common difference be d

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$\sf{\red{\boxed{\bold{a_n = a + ( n - 1 ) d }}}}$

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Acc. to the first condition :-

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a10 = a + (10 - 1)d

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a10 = a + 9d

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Acc. to the second statement :-

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a15 = a + (15 - 1)d

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a15 = a + 14d

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Acc. to the question :-

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10(a + 9d) = 15(a + 14d)

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10a + 90d = 15a + 210d

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90d - 210d = 15a - 10a

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-120d = 5a

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a = -120d/5

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a = -24d ..........( i )

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• Now we will put the value of a from eq ( i ) the given statement

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a25 = a + (25 - 1)d

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a25 = a + 24d

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a25 = -24d + 24d (from Eq. 1)

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a25 = 0

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⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀......Hence Proved