Question

Let AP(a;b) denotes the set of all the terms of an infinite arithmetic progression with the first term a and common difference d if AP(13)

Answer 1

First series is {1,4,7,10,13,..}

Second series is {2,7,12,17,.}

Third series is {3,10,17,24,}

See the least number in the third series which leaves remainder 1 on dividing by 3 and leaves remainder 2 on dividing by 5.

⇒52 is the least number of third series which leaves remainder 1 on dividing by 3 and leaves remainder 2 on dividing by 5

Now, A=52

D is L.C. M. of (3,5,7)=105

⇒A+D=52+105=157.