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In the natural numbers from 10 to 250, how many are divisible by 4? - Algebra

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प्रश्न

In the natural numbers from 10 to 250, how many are divisible by 4?

योग

उत्तर

The least positive natural number from 10 to 250 divisible by 4 is 12.
The sequence divisible by 4 is 12, 16, 20, .... , 248.
Now,

\[t_n = a + \left( n - 1 \right)d\]

\[ \Rightarrow 248 = 12 + \left( n - 1 \right)\left( 4 \right)\]

\[ \Rightarrow 248 = 12 + 4n - 4\]

\[ \Rightarrow 248 = 8 + 4n\]

\[ \Rightarrow 248 - 8 = 4n\]

\[ \Rightarrow 4n = 240\]

\[ \Rightarrow n = 60\]

Hence, 60 numbers are divisible by 4.
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अध्याय 3: Arithmetic Progression - Practice Set 3.2 [पृष्ठ ६६]

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बालभारती Algebra (Mathematics 1) [English] 10 Standard SSC Maharashtra State Board
अध्याय 3 Arithmetic Progression
Practice Set 3.2 | Q 9 | पृष्ठ ६६

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