Question

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Good morning guy
Help me
if five times the 5th term
of an A.P. is equal to eigth times its 8th term,then show that its 13th term is zero​

Answer 1

GOOD MORNING!!,

Here is your answer,

Let first term be a and common difference be d,

According to the question,

5(Fifth term)=8(Eighth term)

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

5a+20d=8a+56d

3a=-36d

===) a = -12d. --------(¹)

Thirteenth term

= a + 12d

= -12d +12d. (From equation ¹)

= 0

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Answer 2

Heya

_______________________________

Nth term in an A.p is given be a +( n - 1)d

=>

5th term is a + 4d

,

8th term is a + 7d

And

13th term is a + 12d

ACCORDING TO THE QUESTION

5× ( a + 4d ) = 8 × ( a + 7d )

=>

5a - 8a + 20d - 56d = 0

=>

-3a - 36d = 0

=>

3a + 36d = 0

=>

a + 12d = 0

Hence 13th term is a + 12d = 0