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Question
Justify whether it is true to say that the following are the nth terms of an AP.
2n – 3
Options
True
False
Solution
This statement is True.
Explanation:
Here,
an = 2n – 3
Put n = 1,
a1 = 2(1) – 3
= –1
Put n = 2,
a2 = 2(2) – 3
= 1
Put n = 3,
a3 = 2(3) – 3
= 3
Put n = 4,
a4 = 2(4) – 3
= 5
List of number becomes –1, 1, 3, 5....
Here, a2 – a1 = 1 – (–1) = 1 + 1 = 2
a3 – a2 = 3 – 1 = 2
a4 – a3 = 5 – 3 = 2
∵ a2 – a1 = a3 – a2 = a4 – a3 = ...........
Hence, 2n – 3 is the nth term of an AP.
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