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प्रश्न
Justify whether it is true to say that the following are the nth terms of an AP.
1 + n + n2
विकल्प
True
False
उत्तर
This statement is False.
Explanation:
Here,
an = 1 + n + n2
Put n = 1,
a1 = 1 + 1 + (1)2
= 3
Put n = 2,
a2 = 1 + 2 + (2)2
= 1 + 2 + 4
= 7
Put n = 3,
a3 = 1 + 3 + (3)2
= 1 + 3 + 9
= 13
So, the list of number becomes 3, 7, 13,...
Here, a2 – a1 = 7 – 3 = 4
a3 – a2 = 13 – 7 = 6
∴ a2 – a1 ≠ a3 – a2
Since, the difference of the successive term is not same.
So it does not form an AP.
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