Question

Find the sum of all natural number less than 200 which are divisible by 7.​

Answer 1

The sum of all natural number less than 200 which are divisible by 7:

7 + 14 + 21 + 28 + ........... + 196

Here, first term (a) = 7, common difference (d) = 41 - 7 = 7

We have to find, the sum of all natural number less than 200 which are divisible by 7.

Solution:

Let n be the nth term of an AP.

7 + (n - 1)7 = 196 [ ∵ $a_{n}$ = a + (n -1)d]

⇒ (n - 1)7 = 196 - 7 = 189

⇒ n - 1 = 27

⇒ n = 28

We know that

The sum of nth term of an AP.

$S_{n} =\dfrac{n}{2} (a + a_{n})$

⇒ $S_{n} =\dfrac{28}{2} (7 + 196)$

⇒ $S_{n} = 14 (203)=2842$

Thus, the sum of all natural number less than 200 which are divisible by 7 is "2842".

Answer 2

Answer:

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