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