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Arithmetic Progressions — Maths STD 10 — Question

CBSE BoardEnglish MediumSTD 10MathsArithmetic Progressions2 Marks
Question
How many two-digit numbers are divisible by 3?
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Answer

The two -digit numbers divisible by 3 start from 12,15,18,21,...,99
Here,
$a=12$
$d=3$
$a_n=a+(n-1)d$
$\Rightarrow$ $99=12+(n-1)(3)$
$\Rightarrow$$ 99=12+3n-3$
$\Rightarrow$ $90=3n$
$\Rightarrow$ n=30
Thus, 30 two-digit numbers are divisible by 3.

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