Question

In an A.P 5 times of 4th term is equal to 4 times of 5th term. Then find 9th term in A.P

Answer 1

We know that,
$\bf a_{4} = a + 3d \\ \bf And, a_{5} = a + 4d$

Given,

$5(a + 3d) = 4(a + 4d) \\ 5a + 15d = 4a + 16d \\ 5a - 4a = 16d - 15d \\ \bf a = d$

$a_{9} = a + 8d$

Since, a = d [Solved above]

We can also write it as,

$a_{9} = a + 8(a) \\ a_{9} = a + 8a \\ a_{9} = 9a$

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