Question

if five times the the fifth term of an AP is equal to 8 times the 8th term,show that it's 13 th term is 0

Answer 1

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Here is your answer.....☺

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➡ Fifth term of A.P = a + ( 5 - 1 )d = a + 4d

➡ Eighth term of A.P = a + ( 8 - 1)d = a + 7d.

To prove : 13 th term = 0
=> a + ( 13 - 1 ) d = 0
=> a + 12d = 0

According to question we have,

=> 5( a + 4d) = 8 ( a + 7d)
=> 5a + 20d = 8a + 56d
=> 20d - 56d = 8a - 5a
=> -36d = 3a
=> 3a + 36d = 0
=> 3( a + 12d) = 0
=> a + 12d = 0.

Hence, proved.

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➡ 13 th term of A.P is equal to 0.

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Hope this helps you......✨✨✨

Answer 2

5th term = a + 4d
8th term = a + 7d

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According to the given informations,

5th term = 8th term

5(a + 4d) = 8(a + 7d)

5a + 20d = 8a + 56d

3a = -36d

a = -12d ------1equation

Now,

13th term = a + 12d

a + 12d

Putting the value of a from 1equation,

=> -12d + 12d

=> 0


I hope this will help you

-by ABHAY