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

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Solution

The series formed by all the integers between 100 and 550 which are divisible by 9 is 108, 117, 123, ...., 549
Let there be n terms in the A.P. then, the nth term is 549
549 = a + (n - 1)d
549 = 108 + (n - 1)9
$\Rightarrow n = 50$
Then,
$S_{n} = \frac{n}{2} [a + l] S_{50} = \frac{50}{2} [108 + 549] = 16425$

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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 $5$ .