Question

Let AP(a; d) denote the set of all the terms of an infinite arithmetic progression with first term a and common difference d > 0. If AP(1; 3) ⌒ AP(2; 5) ⌒ AP(3; 7) = AP (a;d) then a + d equals_____

Answer 1

Answer:

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.

October 15, 2019

Step-by-step explanation:

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Answer 2

Answer:

refers to the attachment