Question

find the sum of all integers between 50 and 500 which are divisible by 7 ​

Answer 1

GIVEN :-

The sum of all integers between 50 and 500 which are divisible by 7

We can solve this by applying the concept of Aritematic Progression.

Here we got that ,

First Term ( a ) = 56

Common difference ( d ) = 7

Last term ( l ) = 497

TO FIND :- Sum of all the terms

ANSWER :-

$a_n = a + (n - 1)d \\ \\ \\ \implies497 = 56 + (n - 1)7 \\ \\ \\ \implies441 = (n - 1)7 \\ \\ \\ \implies n - 1 = 63 \\ \\ \\ \implies \boxed{n = 64}$

Now we should use this below formula to find the Sum :-

$s_n = \frac{n}{2} (a + l) \\ \\ \\ \\ = \frac{64}{2} (56 + 497) \\ \\ \\ = 32 \times 553 \\ \\ \\ = {\boxed {\boxed{ 17,696}}}$

Hence The Answer is 17,696