Question

find the sum of all natural number lying between 100 and 1000 which are multiples of 5.

Answer 1

Answer:2850

Step-by-step explanation:Natural number between 100 and 1000 and multiples of 5 are:105,110,115,120,125,130,135,150,155,160,165,170,175,180,185,190,195 and their sum is 2850

Answer 2

$\Large{\textbf{\underline{\underline{According\:to\:the\:Question}}}}$

Natural numbers are follows

105,110,115,120,...............,995

Here we have

First term(a) = 105

Common difference (d) = 110 - 105 = 5

Using formula we have

${\boxed{\sf\:{a_{n}=a+(n-1)d}}}$

Hence,

a + (n - 1)d = 995

Putting the values :-

105 + (n - 1)5 = 995

(n - 1)5 = 995 - 105

(n - 1)5 = 890

$\tt{\rightarrow n-1=\dfrac{890}{5}}$

n - 1 = 178

n = 178 + 1

n = 179

Now,

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

$\tt{\rightarrow S_{179}=\dfrac{179}{2}[2(105)+(179-1)(5)]}$

$\tt{\rightarrow S_{179}=\dfrac{179}{2}[2(105)+(178)(5)]}$

= 179[105 + (89) × 5]

= 179[105 + 445]

= 179 × 550

= 98450