Question

Find the number of numbers lying between 146 and 300 which are divisible by both 3 and 5.

Answer 1

Answer:

The numbers lying between 146 and 300 which are divisible by both 3 and 5 are 150, 165, 180, 195, 210, 225, 240, 255, 270 and 285.

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Answer 2

The numbers between 146 and 300 which is divisibe by 3 and 5 will be a multiple of 15(3×5).

Therefore the numbers are,

150,165,180……..,285,300

From the series, it is clear that it is an arithmetic progression having:

• First term (a₁) = 150
• Common difference (d) = 15
• Last term (aₙ) = 300

Now,

we have to find the number of terms in the expansion.

It can be determined by the equation,

$\boxed{\bold{n=[\frac{a_n-a_1}{d}]+1}}$

Applying the values to the equation,

$\bold{n=[\frac{300-150}{15}]+1}$

$\bold{\implies{n=[\frac{150}{15}]+1}}$

$\bold{\implies{n=10+1}}$

$\boxed{\bold{\therefore{n=11}}}$

Hence,

There are 11 numbers between 146 and 300 which are divisible by 3 and 5.