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Question
How many terms are there in the series `3/4, 1, 1 1/4, ........., 3`?
Solution
The given series is `3/4, 1, 1 1/4 , ........., 3`
`=> 3/4, 1, 5/4, ........., 3`
`1 - 3/4 = 1/4, 5/4 - 1 = 1/4,` etc
Thus, the given series is an A.P. with first term a = `3/4` and common difference d = `1/4`.
Last term = l = 3
`3/4 +(n - 1)(1/4) = 3`
`=> (n - 1)xx 1/4 = 3 - 3/4`
`=> (n - 1) xx 1/4 = 9/4`
`=>` n – 1 = 9
`=>` n = 10
Thus, there are 10 terms in the given series.
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