Question

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

Answer 1

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. :

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