Find the sum of all integers between 100 and 550, which are divisible by 9.

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Solution

The integers between 100 and 550 that are divisible by 9 are:
108, 117...549
Here, we have:
$a = 108 d = 9 a_{n} = 549 \Rightarrow 108 + (n - 1) (9) = 549 \Rightarrow 9 n - 9 = 441 \Rightarrow 9 n = 450 \Rightarrow n = 50 S_{n} = \frac{n}{2} [2 a + (n - 1) d] \Rightarrow S_{50} = \frac{50}{2} [2 \times 108 + (50 - 1) \times 9] \Rightarrow S_{50} = 25 (657) = 16425$

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Q. Find the sum of all even integers between 100 and 550 , which are divisible by 9.

Find the sum of

(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 $5$ .