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Question
Find the sum of those integers between 1 and 500 which are multiples of 2 as well as of 5.
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Solution
Since, multiples of 2 as well as of 5 = LCM of (2, 5) = 10
∴ Multiples of 2 as well as of 5 between 1 and 500 is 10, 20, 30,..., 490
Which form an AP with first term (a) = 10
And common difference (d) = 20 – 10 = 10
nth term an = Last term (l) = 490
∴ Sum of n terms between 1 and 500,
Sn = `n/2[a + 1]` ...(i)
∵ an = a + (n – 1)d = l
⇒ 10 + (n – 1)10 = 490
⇒ (n – 1)10 = 480
⇒ n – 1 = 48
⇒ n = 49
From equation (i),
S49 = `49/2(10 + 490)`
= `49/2 xx 500`
= 49 × 250
= 12250
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