QJEEM23Ma170f: JEE Main 2023 Mathematics - Class 11 JEEM23Ma170f Solution: The sum of the common terms of the following three arithmetic…

Question

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The sum of the common terms of the following three arithmetic progressions.

$3, 7, 11, 15, \dots ., 399$ ,

$2, 5, 8, 11, \dots ., 359$ and

$2, 7, 12, 17, \dots ., 197$ ,

is equal to _____________.

Accepted Answer

\begin{array}{ll} 3, 7, 11, 15, \dots \dots \dots . .399 : & d_{1} = 4 \\ 2, 5, 8, 11, \dots \dots \dots \dots, 359 : & d_{2} = 3 \\ 2, 7, 12, 17, \dots \dots, 197 : & d_{3} = 5 \\ LCM (d_{1}, d_{2}, d_{3}) = 60 \end{array}

Common terms are 47, 107, 167

Sum

=321

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