Question

How many terms are there in the series `3/4, 1, 1 1/4, ........., 3`?

Answer 1

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.