Answer:
17822
Step-by-step explanation:
The number that are divisible by 7 between 30 and 500 are as follows :
35, 42,49,.....,497
It will form an AP with first term, a = 35 and common difference, d = 7
Let there are n terms in the AP.
nth term of an AP is given by :
[tex]a_n=a+(n-1)d[/tex]
Putting all the values,
[tex]497=35+(n-1)7\\\\462=(n-1)7\\\\n-1=66\\\\n=67[/tex]
Now, the sum of n terms of an AP is given by :
[tex]S_n=\dfrac{n}{2}[2a+(n-1)d][/tex]
Putting all the values,
[tex]S_n=\dfrac{67}{2}[2(35)+(67-1)7]\\\\S_n=17822[/tex]
Hence, the sum of the numbers that are divisible by 7 between 30 and 500 is 17822.
