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8. Sequences and Series
hard
Let $3,7,11,15, \ldots, 403$ and $2,5,8,11, \ldots, 404$ be two arithmetic progressions. Then the sum, of the common terms in them, is equal to.....................
A
$6696$
B
$6697$
C
$668$
D
$6699$
(JEE MAIN-2024)
Solution
$3,7,11,15, \ldots ., 403$
$2,5,8,11, \ldots ., 404$
$\operatorname{LCM}(4,3)=12$
$11,23,35, \ldots . \text { let }(403)$
$403=11+(n-1) \times 12$
$\frac{392}{12}=n-1$
$33 \cdot 66=n$
$n=33$
$\operatorname{Sum} \frac{33}{2}(22+32 \times 12)$
$=6699$
Standard 11
Mathematics
