JEE MAIN - Mathematics (2023 - 1st February Evening Shift - No. 20)
The sum of the common terms of the following three arithmetic progressions.
$$3,7,11,15, \ldots ., 399$$,
$$2,5,8,11, \ldots ., 359$$ and
$$2,7,12,17, \ldots ., 197$$,
is equal to _____________.
Answer
321
Explanation
$$
\begin{array}{ll}
3,7,11,15, \ldots \ldots \ldots . .399 : & \mathrm{~d}_1=4 \\\\
2,5,8,11, \ldots \ldots \ldots \ldots, 359 : & \mathrm{~d}_2=3 \\\\
2,7,12,17, \ldots \ldots, 197 : & \mathrm{~d}_3=5 \\\\
\operatorname{LCM}\left(\mathrm{d}_1, \mathrm{~d}_2, \mathrm{~d}_3\right)=60 &
\end{array}
$$
Common terms are 47, 107, 167
Sum $=321$
Common terms are 47, 107, 167
Sum $=321$
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