Question

# Statement 1: The nth term of an AP can not be n2+1. Statement 2: 0 is a term of the AP 31, 28, 25….

A
Both statement 1 and
statement 2 are true.
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B
Statement 1 is true, while statement 2 is false.
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C
Statement 1 is false, while statement 2 is true.
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D
Both statement 1 and statement 2 are false.
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Solution

## The correct option is B Statement 1 is true, while statement 2 is false.Statement 1: The nth term of an AP cannot be n2 + 1. nthterm=n2+1. 1stterm=1×1+1 = 2 2ndterm=2×2+1 = 4+1 =5 3rdterm=3×3+1 = 10 common difference = 2nd term - 1st term = 3 ≠ 3rd term - 2nd term = 5. That means Statement 1 is true. Statement 2: 0 is a term of the AP 31, 28, 25…. nth term = a + (n - 1)d. 1st term (a) = 31 2nd term = 28 common difference (d) = 2nd term - 1st term = 28 - 31 = -3 Let’s assume that nth term of this AP is 0. nth term = a + (n - 1)d = 0 = 31 - (n - 1)3 = 0 ⇒n=343 n should be a natural number. In this case n is a fraction that means 0 is not a term in given AP.

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