Question

find the sum of 3 digit natural nos which are multiples of 7​

Answer 1

Answer:

The sum of all three digit natural numbers which are multiples of 7 is 70336.

To find:

• Sum of three digit natural numbers which are multiples of 7.

Solution:

The three digit numbers which are multiples of 7 are

105, 112, 119, ... , 994

It forms an A.P. with first term (a) = 105 and common difference (d) = 7

Here, Last term $\sf{(t_{n})}$ = 994

$\boxed{\sf{t_{n}=a+(n-1)d}}$

$\sf{\implies}$ 994 = 105 + (n - 1) 7

$\sf{\implies}$ 7 (n - 1) = 994 - 105

$\sf{\implies}$ 7 (n - 1) = 889

$\sf{\implies}$ n - 1 = 889/7

$\sf{\implies}$ n = 127 + 1

$\sf{\implies}$ n = 128

Sum of all three digit natural numbers which are multiples of 7 can be find the sum of n terms of an A.P.

$\boxed{\sf{S_{n}=\dfrac{n}{2}[t_{1}+t_{n}]}}$

$\sf{\therefore{S_{128}=\dfrac{128}{2}[105+994]}}$

$\sf{\therefore{S_{128}=64\times1099}}$

$\sf{\therefore{S_{128}=70336}}$

The sum of all three digit natural numbers which are multiples of 7 is 70336.