In an A.P., Ten Times of Its Tenth Term is Equal to Thirty Times of Its 30th Term. Find Its 40th Term. - Mathematics
In an A.P., ten times of its tenth term is equal to thirty times of its 30th term. Find its 40th term.
The general term of an A.P is given by
`t_n = a + (n -1)d`
`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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