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JEE Main20231 Feb 2023Evening ShiftMathematicsSequences and SeriesActual

The sum of the common terms of the following three arithmetic progressions. 3 , 7 , 11 , 15 , … … … … , 399 2 , 5 , 8 , 11 , . . . . . . . . . 359 and 2 , 7 , 12 , 17 , … … , 197 , is equal to _____ .

Correct answer

0

Step-by-step solution

We have, S 1 :   2 , 5 , 8 , 11 , . . . , 359 Common difference is d 1 = 3 S 2 :   3 , 7 , 11 , 15 . . . , 399 Common difference is d 2 = 4 S 3 : 2 , 7 , 12 , 17 . . . , 197 Common difference is d 3 = 5 Now taking LCM of common difference we get, LCM d 1 ,   d 2 ,   d 3 = 60 So, common terms are 47 , 107 , 167 , Hence, the sum will be 47 + 107 + 167 = 321 .

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