Question

Find the sum of all natural numbers between 250 and 1000,which are exactly divisible by 300.
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Answer 1

Solution :

$\bf{\red{\underline{\bf{Given\::}}}}$

The sum of all natural numbers between 250 and 1000, which are exactly divisible by 3.

$\bf{\red{\underline{\bf{To\:find\::}}}}$

The sum.

$\bf{\red{\underline{\bf{Explanation\::}}}}$

Here, these number which are divisible by 3 between 250 and 1000.

252,255,258,261.....................999

$\underline{\underline{\bf{Using\:formula\:of\;A.P.}}}}}$

We know that formula of the last term of an A.P;

$\boxed{\bf{a_{n}=a+(n-1)d}}}}$

• a is the first term.
• d is the common difference.
• n is the term of an A.P.

A/q

$\longrightarrow\sf{999=252+(n-1)3}\\\\\longrightarrow\sf{999=252+3n-3}\\\\\longrightarrow\sf{999=249+3n}\\\\\longrightarrow\sf{3n=999-249}\\\\\longrightarrow\sf{3n=750}\\\\\longrightarrow\sf{n=\cancel{\dfrac{750}{3} }}\\\\\\\longrightarrow\sf{\orange{n=250}}$

Now;

We know that formula of the last term sum of an A.P;

$\boxed{\bf{S=\frac{n}{2} \big[a+l\big]}}}}$

$\longrightarrow\sf{S=\cancel{\dfrac{250}{2} }\bigg[252+999\bigg]}\\\\\\\longrightarrow\sf{S=125\big[1251\big]}\\\\\\\longrightarrow\sf{S=125\times 1251}\\\\\\\longrightarrow\sf{\orange{S=156375}}$

Answer 2

Answer:

$\implies$ n = 250

$\implies$ S = 156375.

$\large\underline\mathrm{Given:-}$

• The sum of all natural numbers between 250 and 1000,which are exactly divisible by 3.

$\large\underline\mathrm{To \: find}$

• The sum of natural number.

$\large\underline\mathrm{Solution}$

The number which are divible by 3 between 250 and 1000.

$\implies$ 252, 255, 258, 261......... 999.

Using formula of A.P

We know that the last of an A.P

$\implies$ A(n) = a + (n - 1)d

$\implies$ a = 252

$\implies$ d = 3

$\implies$ n = ?

$\implies$ a(n) = 999

So,

$\implies$ 999 = 252 + (n - 1)3

$\implies$ 999 = 252 + 3n - 3

$\implies$ 999 = 249 + 3n

$\implies$ 3n = 999 - 249

$\implies$ 3n = 750

$\implies$ n = 750/3

$\implies$ n = 250

Now,

The last terms sum of an A.P.

$\implies$ S = n/2(a + l)

$\implies$ S = 250/2(252 + 999)

$\implies$ S = 125 × 1251

$\implies$ S = 156375.