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Arithmetic Progressions
CH05 Question Bank
CBSE_CH05_QUESTION_BANK
Grade 10
Question:
Assertion (A): If $S_n=2n^2+3n$ is the sum of the first $n$ terms of an AP, the AP itself is $5,9,13,17,\ldots$ Reason (R): $a_1=S_1$ and $a_n=S_n-S_{n-1}$ for $n\geq2$.
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: Recovering the AP from a quadratic sum expression.
$a_1=S_1=2+3=5$. $a_2=S_2-S_1=(8+6)-5=14-5=9$. $a_3=S_3-S_2=(18+9)-14=27-14=13$. So the AP is $5,9,13,17,\ldots$ — A is true. [0.5 Mark]
R correctly states exactly the method used to recover the terms, 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.
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