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Find the sum of those integers between 1 and 500 which are mul

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

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Text solutionVerified

Integers which are multiples of

2

as well as

5

are multiples of

10

i.e.,

10, 20, 30, 490

.
[Between

1

and

500

]

∴ a = 10, d = 10, a_{n} = 490

Now,

a_{n} = 490 [a_{n} = a + (n - 1) d]

\to a + (n - 1) d = 490

\to 10 + (n - 1) 10 = 490

\to 1 + (n - 1) = \frac{490}{10}

\to n = 49

S_{n} = \frac{n}{2} [2 a + (n - 1) d]

S_{49} = \frac{49}{2} [2 \times 10 + (49 - 2) 10]

= \frac{49}{2} \times [2 + 48] = 49 \times 5 \times 50

\to S_{49} = 12250

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Question Text	Find the sum of those integers between 1 and 500 which are multiples of 2 as well as of 5.
Answer Type	Text solution:1
Upvotes	150