the sum of the numbers from 300 to 700 which are divisible by 3 or 5 is plz friends give single answer plz answer fast

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the sum of the numbers from 300 to 700 which are divisible by 3 or 5 is plz friends give single answer plz answer fast

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1 month 2021-08-14T00:14:25+00:00 1 Answer 1 views 0

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    2021-08-14T00:16:09+00:00

    Answer:

    The sum of the numbers from 300 to 700 which are divisible by 3 or 5 i. e. 15, LCM of 3 & 5 is 13365.

    Step-by-step-explanation:

    The numbers from 300 to 700 which are divisible by 15 i. e. LCM of 3 and 5 are 300, 315,…, 690.

    This is an A.P.

    \bullet\sf\:a\:=\:300\\\\\\\bullet\sf\:d\:=\:15\\\\\\\sf\:Now,\\\\\\\pink{\sf\:t_n\:=\:a\:+\:(\:n\:-\:1\:)\:d}\sf\:\:\:-\:-\:[\:Formula\:]\\\\\\\implies\sf\:690\:=\:300\:+\:(\:n\:-\:1\:)\:\times\:15\\\\\\\implies\sf\:690\:-\:300\:=\:(\:n\:-\:1\:)\:\times\:15\\\\\\\implies\sf\:390\:=\:(\:n\:-\:1\:)\:\times\:15\\\\\\\implies\sf\:n\:-\:1\:=\:\cancel{\frac{390}{15}}\\\\\\\implies\sf\:n\:-\:1\:=\:26\\\\\\\implies\sf\:n\:=\:26\:+\:1\\\\\\\implies\boxed{\red{\sf\:n\:=\:27}}

    Now, we know that,

    \pink{\sf\:S_n\:=\:\frac{n}{2}\:[\:a\:+\:l\:]}\sf\:\:\:-\:-\:[\:Formula\:]\\\\\\\implies\sf\:S_{27}\:=\:\frac{27}{2}\:[\:300\:+\:690\:]\\\\\\\implies\sf\:S_{27}\:=\:\frac{27}{\cancel2}\:\times\:\cancel{990}\\\\\\\implies\sf\:S_{27}\:=\:27\:\times\:495\\\\\\\implies\boxed{\red{\sf\:S_{27}\:=\:13365}}

    The sum of the numbers from 300 to 700 which are divisible by 15 i. e. LCM of 3 and 5 is 13365.

    \\

    Additional Information:

    1. Arithmetic Progression:

    1. In a sequence, if the common difference between two consecutive terms is constant, then the sequence is called as Arithmetic Progression ( AP ).

    2. \sf\:n^{th} term of an AP:

    The number of a term in the given AP is called as \sf\:n^{th} term of an AP.

    3. Formula for \sf\:n^{th} term of an AP:

    \large{\boxed{\red{\sf\:t_{n}\:=\:a\:+\:(\:n\:-\:1\:)\:d}}}

    4. The sum of the first n terms of an AP:

    The addition of either all the terms of a particular terms is called as sum of first n terms of AP.

    5. Formula for sum of the first n terms of A. P. :

    \large{\boxed{\red{\sf\:S_{n}\:=\:\frac{n}{2}\:[\:2a\:+\:(\:n\:-\:1\:)\:d\:]}}}

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