Question

QUESTION:

Find the sum of all three digit numbers, which are multiples of 9.
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Answer 1

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$\huge\underline\mathfrak\green{solution:-}$

List of three digit no.s that are multiples of 9 are:- 108, 117, 126.....999

Here,

$\tt a = 108$

$\tt d = 9$

$\tt an = a + (n - 1)d$

$\blue\longrightarrow\tt 999 = 108+ (n - 1)9$

$\blue\longrightarrow\tt (n - 1)9 = 999- 108$

$\blue\longrightarrow\tt n - 1 = \frac{891}{9}$

$\blue\longrightarrow\tt n = 99 + 1$

$\blue\longrightarrow\tt n = 100$

Again,

Sn

$\red\longrightarrow\tt \frac{n}{2} (a + l)$

$\red\longrightarrow\tt \frac{100}{2} (108 + 999)$

$\red\longrightarrow\tt \frac{100}{2} \times 1107$

$\red\longrightarrow\tt 50 \times 1107$

$\red\longrightarrow\tt 5535$

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