Not the exact question you were looking for?

Paste your question to our Mathbee AI Mentor below to get an instant step-by-step solution.

Arithmetic Progressions
CH05 Question Bank
CBSE_CH05_QUESTION_BANK
Grade 10

Question:

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.
Mathbee AI Mentor (Free Demo)

Confused by the solution? Ask the AI to explain a specific step, tell you where you went wrong, or break down the key trap in this question.

Master Arithmetic Progressions with Mathbee

Practice this topic under real exam conditions with strict timers, or ask our AI Mentor to explain the concepts step-by-step.

Start Practicing for Free