Question

find the sum of all the naturales number between 150 and 200 which are divisible by 7.​

Answer 1

Step-by-step explanation:

Solution

The numbers from 150 to 200 divisible by 7 are 154,161 ,168,…., 196 <br> Here,

a= 154, d= 7

and

t_(n) = 196

<br>

t_(n) = a+ ( n -1)d

…(Formula ) <br>

:. 196 = 154 + ( n-1) xx 7

…(Substituting the values ) <br>

:. 196 - 154 = ( n-1) xx 7

<br>

:. ( 42)/(7) = n-1

:. n -1 = 6

:. n = 7

<br> Now, we find the sum of 7 numbers. <br>

S_(n) = (n)/(2) [t_(1) + t_(n)]

...(Formula ) <br>

= ( 7)/(2) [ 154 + 196)

<br>

= ( 7)/(2) xx 350

<br>

= 7 xx 175

<br>

= 1225

Answer 2

Answer:

The sum is 1225

Step-by-step explanation:

The numbers from 150 to 200 divisible by 7 are 154,161 ,168,…., 196

Here, a=154,d=7 and tn =196

tn=a+(n−1)d

∴196=154+(n−1)×7

∴196−154=(n−1)×7

∴42/7=n−1

.:n−1=6

∴n=7

Now, we find the sum of 7 numbers.

Sn=(n/2)[t1+tn]

=(7/2)×[154+196)

=7/2×350

=7×175

=1225