Question

Find the sum of all natural numbers between 250 and 1000 which are exatly divisible by 3.

Answer 1

★ GiveN :

A.P : 252, 255, 258, 261 ........ 999

First term (a) = 252

Common Difference (d) = 3

Last term (An or L) = 999

$\rule{200}{1}$

★ To FinD :

We have to find the sum of all natural numbers between 250 and 1000 which are exatly divisible by 3.

$\rule{200}{1}$

★ SolutioN :

Firstly, we will calculate the number of terms.

So,

$\Large{\implies{\boxed{\boxed{\sf{A_n = a + (n - 1)d}}}}}$

★ Putting Values ★

$\sf{\dashrightarrow 999 = 252 + (n - 1)3} \\ \\ \sf{\dashrightarrow 999 = 252 + 3n - 3} \\ \\ \sf{\dashrightarrow 999 = 249 + 3n} \\ \\ \sf{\dashrightarrow 3n = 999 - 249} \\ \\ \sf{\dashrightarrow 3n = 750} \\ \\ \sf{\dashrightarrow n = \frac{\cancel{750}}{\cancel{3}}} \\ \\ \sf{\dashrightarrow n = 250} \\ \\ \Large{\implies{\boxed{\boxed{\sf{n = 250}}}}}$

$\rule{150}{2}$

Now,

$\Large{\implies{\boxed{\boxed{\sf{S_n = \frac{n}{2}(a + L)}}}}}$

★ Putting Values ★

$\sf{\dashrightarrow S_{250} = \frac{250}{2} (252 + 999)} \\ \\ \sf{\dashrightarrow S_{250} = \frac{\cancel{250}}{\cancel{2}} \times 1251} \\ \\ \sf{\dashrightarrow S_{250} = 125 \times 1251 } \\ \\ \sf{\dashrightarrow S_{250} = 156375} \\ \\ \Large{\implies{\boxed{\boxed{\sf{S_{250} = 156375}}}}}$

Answer 2

$\huge \mathfrak \red{answer}$

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Question:

Find the sum of all natural numbers between 250 and 1000 which are exatly divisible by 3.

_____________________________

Step to step explanation:

the numbers between 250 and 1000 which are exatly divisible by 3 are 252,255,258,..............999

then

the AP whose term is

• a = 252
• common difference d = 3
• last term = 999

now we know that formula

$\bf{{ \boxed{ \green{ \tt{l= a + (n - 1)d \: }}}}}$

$= \rm{999 = 252 + (n - 1)3}$

$= \rm{999 - 252 = 3(n - 1)}$

$\rm{n = 250}$

_____________________________

Again we know that other formula of AP

$\bf{ \boxed{ \blue{ \tt{sn = \frac{n}{2}(a + l) \: }}}}$

$= \tt{ \frac{252}{2}(250 + 999)}$

$= \tt{125 \times 1251}$

$= \tt{156375}$

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do you know what is AP?

• AP means arithmetic progession

• arithmetic progession is nothing but the it is a sequence of the numbers such that the difference between the consecutive term is constant

• where the initial term a and the common difference d are real numbers

I hope it's help uh