Question 31
Find the sum of first seven numbers which are multiples of 2 as well as of 9.

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Solution

To find the sum of first seven numbers which are multiples of 2 as well as of 9, take LCM of 2 and 9; which is 18.
So, the numbers are 18, 36, 54, ....
Here, first term, a = 18, common difference, d = 36 – 18 = 18
$S_{n} = \frac{n}{2} [2 a + (n - 1) d], S_{7} = \frac{7}{2} [2 (18) + (7 - 1) 18]$
$= \frac{7}{2} [36 + 6 \times 18] = 7 (18 + 3 \times 18)$
$= 7 (18 + 54) = 7 \times 72 = 504$

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Find the sum of those integers between 1 and 500 which are multiple of 2 as well as of 5.

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(i) all integers between $100$ and $550$ , which are divisible by $9$ .
(ii) all integers between $100$ and $550$ which are not divisible by $9$ .
(iii) all integers between $1$ and $500$ which are multiples of $2$ as well as of $5$ .
(iv) all integers from $1$ to $500$ which are multiplies $2$ as well as of $5$ .
(v) all integers from $1$ to $500$ which are multiples of $2$ or $5$ .

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Method of Finding LCM

Standard X Mathematics

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Question 31 Find the sum of first seven numbers which are multiples of 2 as well as of 9.

Question 31
Find the sum of first seven numbers which are multiples of 2 as well as of 9.