ASSERTON-REASON:
STATEMENT-1: If $a_{1}, a_{2}, a_{3}, - - - - a_{16}$ is an A.P such that $a_{1} + a_{4} + a_{7} + - - + a_{16} = 147,$ then $a_{1} + a_{6} + a_{11} + a_{16} = 98$
STATEMENT-2: In an A.P the sum of the terms equidistant from the beginning and the end is always same and it is equal to the sum of first and last term

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Statement 1 is true statement 2 is false

Statement 1 is false statement 2 is true

Statement 1 is true statement 2 is true, statement 2 is a correct explanation of statement 1

Statement 1 is true statement 2 is true; statement 2 is not a correct explanation for statement 1

answer is A.

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Detailed Solution

Statement 2 is a property of an A.P so it is true.
$a_{1} + a_{4} + a_{7} + - - + a_{16} = 147,$
$\Rightarrow (a_{1} + a_{16}) + (a_{4} + a_{13}) + (a_{7} + a_{10}) = 147$ $\Rightarrow 3 (a_{1} + a_{16}) = 147$ $\Rightarrow a_{1} + a_{16} = 49.$
$∴ a_{1} + a_{6} + a_{11} + a_{16} = (a_{1} + a_{16}) + (a_{6} + a_{11})$ $= 2 (a_{1} + a_{16}) = 98$