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Question
Write the nth term of the following sequences.
`1/2, 3/4, 5/6, 7/8, 9/10, ...`
Solution
The given sequence is `1/2, 3/4, 5/6, 7/8, 9/10, ...`
The terms in the numerator are 1, 3, 5, 7, 9, …
a = 1 , d = 3 – 1 = 2
an = a + (n – 1) d
an = 1 + (n – 1)2
an = 1 + 2n – 2 = 2n – 1
The terms in the denominator are 2, 4, 6, 8, 10, …
a = 2, d = 4 – 2 = 2
an = a + (n – 1) d
an = 2 + (n – 1)(2)
an = 2 + 2n – 2 = 2n
∴ The nth term of the given sequence is an = `(2"n" - 1)/(2"n")` for all n ∈ N
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