Assertion (A): An AP with a positive common difference can have only positive terms.
Reason (R): A positive common difference means each term is obtained by adding a positive number to the previous term.
Both Assertion (A) and Reason (R) are true, and R is the correct explanation of A.
Both Assertion (A) and Reason (R) are true, but R is NOT the correct explanation of A.
Assertion (A) is true, but Reason (R) is false.
Assertion (A) is false, but Reason (R) is true.
Step-by-Step Solution
Key Concept: R is a correct general fact about how terms are formed, but it does not prevent early terms (before the sequence 'catches up') from being negative if the first term itself is very negative.
A counter-example: the AP $-20,-15,-10,-5,0,5,\ldots$ has a positive common difference $d=5$, but its first several terms are negative — so A is false. [0.5 Mark]
R is a true general statement about how each successive term is formed (by adding $d>0$), even though it does not by itself guarantee all terms are positive. [0.5 Mark]
Correct Answer: Assertion (A) is false, but Reason (R) is true.