AP(1;3)={1,4,7,10......} say S1 AP(2;5)={2,7,12,17,........} say S2 AP(3;5)={3,10,17,24,.....}say S3 S1∩S2={7,22,37,52,....}i.e., AP(7;15) To find the term common to AP(7;15) and AP(3,7) 7+15l=3+7m ∴m=
4+l
7
+2l where l,m ∊ W ⇒l can be 3 ∴m=7 ∴S1∩S2∩S3=AP(52;105) ∴a+d=157