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): If the sum of the first 10 terms of an AP equals the sum of the first 15 terms, the sum of the first 25 terms of that AP must be zero. Reason (R): If $S_p=S_q$ for $p eq q$, then $S_{p+q}=0$.
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: Direct application of the standard identity, with p=10, q=15, p+q=25.
Since $S_{10}=S_{15}$ and $10+15=25$, by the standard result $S_{25}=0$ — A is true. [0.5 Mark]
R correctly states the general identity being applied, so R correctly explains A. [0.5 Mark]
Correct Answer:Both Assertion (A) and Reason (R) are true, and R is the correct explanation of A.
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.