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 _____

Answer 1

$ 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 \,\,\,\, d_3=5 $
$ \operatorname{LCM}\left( d _1, d _2, d _3\right)=60 $
$ \text { Common terms are 47, 107, } 167$
$ \text { Sum }=321 $