Find the sum of those integers between 1 and 500 which are multiples of 2 as well as of 5.

# Find the sum of those integers between 1 and 500 which are multiples of 2 as well as of 5.

1. A
12000
2. B
12100
3. C
12250
4. D
12500

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### Solution:

Clearly, the numbers between 1 and 500 which are multiples of 2 as well as of 5 i.e. which are multiples of 10 are 10,20,30,...,490.
first term a=10, common difference d=10 and last term l=490.
an​=490
⇒a+(n−1)d=490
⇒10+(n−1)×10=490
⇒(n−1)10=480
⇒n−1=48⇒n=49
${S}_{n}=\frac{n}{2}\left[a+{a}_{n}\right]$
$⇒{S}_{49}=\frac{49}{2}\left[10+490\right]=\frac{49}{2}×\left(500\right)=12250$

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