Sum

In an A.P., ten times of its tenth term is equal to thirty times of its 30th term. Find its 40th term.

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#### Solution

The general term of an A.P is given by

`t_n = a + (n -1)d`

Given

`10 x t_10 = 30 xx t_30`

`=> 10 xx (a + 9d) = 30 xx (a + 29d)`

=> a + 9d = 3a + 87d

=> 2a + 78d = 0

=> a + 39d = 0

=> a = -39d

Now `t_40 = a + 39d = -39d + 39d = 0`

Concept: Arithmetic Progression - Finding Their General Term

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