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Home » Find the sum of all natural numbers lying between 100 and 1000, which are multiples of 5.
Find the sum of all natural numbers lying between 100 and 1000, which are multiples of 5.
CBSE | Class 11 | Exercise 9.2 | Maths | NCERT | Sequences and Series
Find the sum of all natural numbers lying between 100 and 1000, which are multiples of 5.

The regular numbers lying somewhere in the range of

    \[100\text{ }and\text{ }1000,\]

which are products of

    \[5,\text{ }are\text{ }105,\text{ }110,\text{ }\ldots \text{ }995.\]

It plainly frames an arrangement in A.P.

Where, the initial term,

    \[a\text{ }=\text{ }105\]

Normal contrast,

    \[d\text{ }=\text{ }5\]

Presently,

    \[\begin{array}{*{35}{l}} a\text{ }+\text{ }\left( n\text{ }-1 \right)d\text{ }=\text{ }995 \\ 105\text{ }+\text{ }\left( n\text{ }\text{ }1 \right)\left( 5 \right)\text{ }=\text{ }995 \\ 105\text{ }+\text{ }5n\text{ }\text{ }5\text{ }=\text{ }995 \\ 5n\text{ }=\text{ }995\text{ }\text{ }105\text{ }+\text{ }5\text{ }=\text{ }895 \\ n\text{ }=\text{ }895/5 \\ n\text{ }=\text{ }179 \\ \end{array}\]

We know,

    \[{{S}_{n}}~=\text{ }n/2\text{ }\left[ 2a\text{ }+\text{ }\left( n-1 \right)d \right]\]

NCERT Solutions Class 11 Mathematics Chapter 9 ex.9.2 - 2

In this manner, the amount of all regular numbers lying somewhere in the range of

    \[100\text{ }and\text{ }1000,\]

which are products of

    \[5,\text{ }is\text{ }98450\]

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