Question

if 9 times the 9th term of an A.P. is equak to 13times its 13th term, show that the 22th term of an A.P. is zero
plzz answer

Answer 1

Heya !!!




Given that,


9 ( 9th term ) = 13 ( 13th term )



9 ( A + 8D ) = 13 ( A + 12D)



9A + 72D = 13A + 156D



13A - 9A + 156D - 72D = 0




4A + 84D = 0


4A = -84D



A = (-84D/4) -------(1)



To prove :-



22 term = 0


=> A + 21D = 0




=> -84D/4 + 21D = 0



=> -84D + 84D/4 = 0



=> 0







HOPE IT WILL HELP YOU...... :-)

Answer 2

Hello friend

Good morning

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To prove, 22th term = 0

Given that,

=>♠️ 9× 9th term = 13 × 13th term

=> ♠️9 x a + 8d = 13 x a + 12d

=>♠️ 9a + 72d = 13a + 156d

=>♠️13a - 9a = -156d + 72d

=>♠️4a = - 84d

=> ♠️a = - 21d

So A.T.Q

To prove 22th term = 0

So LHS = a + 21d

=>♠️LHS = - 21d + 21 d

=> ♠️LHS = 0 = RHS

Hence proved

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