Find the sum of those integers from 1 to 500 | vedclass

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(A) Integers from $1$ to $500$ that are multiples of both $2$ and $5$ are multiples of $	ext{lcm}(2, 5) = 10$.These integers form an arithmetic progr

Vedclass · Accepted Answer

$12750$

Vedclass · Answer

(A) Integers from $1$ to $500$ that are multiples of both $2$ and $5$ are multiples of $	ext{lcm}(2, 5) = 10$.These integers form an arithmetic progression: $10, 20, 30, \ldots, 500$.Here,the first term $a = 10$,the common difference $d = 10$,and the last term $l = 500$.Using the formula for the $n$-th term: $a_n = a + (n - 1)d = l$.$10 + (n - 1)10 = 500$.$(n - 1)10 = 490$.$n - 1 = 49$,so $n = 50$.The sum of $n$ terms is given by $S_n = \frac{n}{2}(a + l)$.$S_{50} = \frac{50}{2}(10 + 500) = 25 	imes 510 = 12750$.

Find the sum of those integers from $1$ to $500$ which are multiples of $2$ as well as of $5$.

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