Mathematics
The nth term of a sequence = 5n2 - 3.
Statement (1): The sequence is an A.P.
Statement (2): If the nth term of a sequence is not linear, the sequence does not form an A.P.
Both the statements are true.
Both the statements are false.
Statement 1 is true, and statement 2 is false.
Statement 1 is false, and statement 2 is true.
A.P.
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Answer
Given, an = 5n2 - 3
⇒ a1 = 5(1)2 - 3 = 5 - 3 = 2
⇒ a2 = 5(2)2 - 3 = 5 × 4 - 3 = 20 - 3 = 17
⇒ a3 = 5(3)2 - 3 = 5 × 9 - 3 = 45 - 3 = 42.
Difference between terms :
⇒ a3 - a2 = 42 - 17 = 25
⇒ a2 - a1 = 17 - 2 = 15
Since, the difference between consecutive terms is not equal. Thus, the sequence is not in an A.P.
So, statement 1 is false.
The general form of an A.P. is an = a + (n - 1)d, which is a linear expression in n.
So, if Tn is not linear in n, then the sequence cannot be an A.P.
So, statement 2 is true.
Hence, option 4 is the correct option.
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Related Questions
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