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

Question

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  (A)  (B)  (C)  (D)

Tardigrade Admin · Accepted Answer

3,7,11,15, ldots ldots ldots ldots, 399 d 1=4 2,5,8,11, ldots ldots ldots ldots ., 359 d 2=3 2,7,12,17, ldots ldots, 197 d3=5 operatornameLCM( d 1, d 2, d 3)=60 text Common terms are 47, 107, 167 text Sum =321

Q. 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 _____

$3, 7, 11, 15, \dots\dots\dots\dots, 399 d_{1} = 4$
$2, 5, 8, 11, \dots\dots\dots\dots ., 359 d_{2} = 3$
$2, 7, 12, 17, \dots\dots, 197 d_{3} = 5$
$LCM (d_{1}, d_{2}, d_{3}) = 60$
$Common terms are 47, 107, 167$
$Sum = 321$

Q. 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 _____

3,7,11,15,…………,399d1​=4 2,5,8,11,………….,359d2​=3 2,7,12,17,……,197d3​=5 LCM(d1​,d2​,d3​)=60 Common terms are 47, 107, 167 Sum =321

Q. 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 _____

$3, 7, 11, 15, \dots\dots\dots\dots, 399 d_{1} = 4$
$2, 5, 8, 11, \dots\dots\dots\dots ., 359 d_{2} = 3$
$2, 7, 12, 17, \dots\dots, 197 d_{3} = 5$
$LCM (d_{1}, d_{2}, d_{3}) = 60$
$Common terms are 47, 107, 167$
$Sum = 321$