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Find the sum of all odd integers between 200 and 300 that are divisible both 3 and 7 .
A. 504
B. 1260
C. 756
D. 810
E. 906

$1$ . Find the sum of all odd integers between $200$ and $300$ that are divisible both $3$ and $7$ . $\newline$ A. $504$ $\newline$ B. $1260$ $\newline$ C. $756$ $\newline$ D. $810$ $\newline$ E. $906$

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Find the sum of a finite geometric series

Full solution

Q.

1

. Find the sum of all odd integers between

200

and

300

that are divisible both

3

and

7

.

\newline

A.

504

\newline

B.

1260

\newline

C.

756

\newline

D.

810

\newline

E.

906

Find LCM: First, find the least common multiple (LCM) of $3$ and $7$ to determine the step size for the numbers we're looking for. $\newline$ LCM of $3$ and $7$ is $3 \times 7 = 21$ .
First Odd Number: Since we're looking for odd numbers, the first number in the range that is divisible by $21$ and is odd is $21 \times 10 + 1 = 211$ .
Largest Odd Number: Now, find the largest odd number less than $300$ that is divisible by $21$ . It's $21 \times 14 - 1 = 294$ .
List Odd Multiples: List all the odd multiples of $21$ between $211$ and $294$ . They are $211$ , $233$ , $255$ , $277$ , and $299$ .
Calculate Sum: Add these numbers together to find the sum. $\newline$ Sum = $211 + 233 + 255 + 277 + 299$ .
Calculate Sum: Add these numbers together to find the sum. $\newline$ Sum = $211 + 233 + 255 + 277 + 299$ . Perform the addition. $\newline$ Sum = $1275$ .

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