Question

STATEMENT-1 : If <$a_n$> is a sequence such that $a_1=1$ and $a_{n+1}=\sin a_n$, then $\underset{n\to \infty }{lim}{a}_n=0$.
STATEMENT-2 : Since $x>\sin x\forall x>0.$

• A. STATEMENT-1 is True, STATEMENT-2 is True; STATEMENT-2 is a correct explanation for STATEMENT-1
• B. STATEMENT-1 is True, STATEMENT-2 is True; STATEMENT-2 is NOT a correct explanation for STATEMENT-1
• C. STATEMENT-1 is True, STATEMENT-2 is False
• D. STATEMENT-1 is False, STATEMENT-2 is True

Answer 1

The correct option is A STATEMENT-1 is True, STATEMENT-2 is True; STATEMENT-2 is a correct explanation for STATEMENT-1

$\underset{n\to \infty }{lim}{a}_{n+1}=\underset{n\to \infty }{lim}\sin a_n=\underset{n\to \infty }{lim}{a}_n$
or $\underset{n\to \infty }{lim}(a_n-\sin a_n)=0$
which is possible only when $\underset{n\to \infty }{lim}{a}_n=0$.
Clearly Assertion is followed by Reason.