Question

find the sum of all natural numbers from 1 to 200 1) which are divisible by 7​

Answer 1

Answer:

2842

Step-by-step explanation:

First of all, we need to find the smallest and greatest multiple of 7 between 1 -200.

Clearly, the smallest multiple is 7.

Let this be the first term "a" of our arithmetic sequence.

And by applying rules of divisibility for 7, we can find that 196 is the greatest multiple of 7 between 1 - 200.

Let this be the last term a_n of our A.P.

The common difference of our A.P. is clearly 7.

The formula for the a_n term of an A.P is:

a_n = a + (n-1) d

In this case:

196 = 7 + (n-1)*7

196 - 7 = 7*(n-1)

189/7 = n-1

n = 28

So 196 is the 28th term of our A.P.

Now, the formula for the sum of n terms of an A.P is:

S_n = [n (a + a_n)]/2

In this case:

S_28 = 28/2 (7+196)

= 14 (203)

= 2842