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

Question

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

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

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

$2, 7, 12, 17, \dots \dots, 197$ , is equal to _____ .

TestHub · Accepted Answer

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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