Arithmetic Progressions
CH05 Question Bank
CBSE_CH05_QUESTION_BANK
Grade 10
Question:
Which of the following is NOT an arithmetic progression?
$-3, -\dfrac12, 2, \dfrac92, \ldots$
$\sqrt2, \sqrt8, \sqrt{18}, \sqrt{32}, \ldots$
$1, 3, 9, 27, \ldots$
$a, a+d, a+2d, a+3d, \ldots$
Step-by-Step Solution
Key Concept: Check whether consecutive differences are constant; a geometric sequence (constant ratio) is not generally an AP.
$\sqrt2,\sqrt8=2\sqrt2,\sqrt{18}=3\sqrt2,\sqrt{32}=4\sqrt2$ — common difference $\sqrt2$, so this IS an AP. [0.5 Mark]
$1,3,9,27$ has differences $2,6,18$ (not constant; it's a GP with ratio 3), so this is NOT an AP. [0.5 Mark]
Correct Answer: $1, 3, 9, 27, \ldots$
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