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Arithmetic Progressions

CH05 Question Bank

CBSE_CH05_QUESTION_BANK

Grade 10

Question:

How many multiples of $4$ lie between $10$ and $250$ (both exclusive)?

$59$
$60$
$61$
$62$

Step-by-Step Solution

Key Concept: Identify the AP of multiples of 4 in this range, then use the nth-term formula to count terms.

The multiples of $4$ in this range form the AP $12,16,20,\ldots,248$, with $a=12,\ d=4,\ l=248$. [0.5 Mark]

$248=12+(n-1)4\Rightarrow n-1=59\Rightarrow n=60$. [0.5 Mark]

Correct Answer: $60$

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