Find the sum of those integers between 1 and 500 which are multiples of 2 as well as of 5. - Sri Chaitanya Infinity Learn Best Online Courses for NCERT Solutions, CBSE, ICSE, JEE, NEET, Olympiad and Class 6 to 12

A
12000
B
12100
C
12250
D
12500

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} [a + a_{n}]

\Rightarrow S_{49} = \frac{49}{2} [10 + 490] = \frac{49}{2} \times (500) = 12250

Solution:

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