Question

Show that the sum of multiples of
of 3 between 1 and 100 is 1683.​

Answer 1

Step-by-step explanation:

3,6,9,.....,96,99

a=3,d=3

an=99

3+(@-1)3=99

3@=99

@=33

sn=(33/2)(6+96)

=( 33/2)×102

=33×51

=1683

hence proved

Answer 2

The sum of multiples of 3 between 1 and 100 = 1683.

Step-by-step explanation:

Since we have given that

1 to 100 with multiple of 3

So, our sequence would be

3,6...........................................99

Here, a = 3 d = 3

and we will first find n:

$99=3+(n-1)3\\\\99=3+3n-3\\\\99=3n\\\\n=\dfrac{99}{3}\\\\n=33$

so, the sum of multiples of 3 between 1 and 100 would be

$S_{33}=\dfrac{33}{2}(3+99)\\\\S_{33}=\dfrac{33\times 102}{2}\\\\S_{33}=1683$

Hence, the sum of multiples of 3 between 1 and 100 = 1683.

# learn more:

An aeroplane travels 3060 km in 10 hours how much time will it take to fly 1683​

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