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If 10 Times the 10th Term of an Ap is Equal to 15 Times the 15th Term, Show that Its 25th Term is Zero. - Mathematics

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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)       { a= 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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अध्याय 11: Arithmetic Progression - Exercises 1

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आर.एस. अग्रवाल Mathematics [English] Class 10
अध्याय 11 Arithmetic Progression
Exercises 1 | Q 33

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