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<p></p>

Correct option is A. 157.00First series is1,4,7,10,13,..Second series is2,7,12,17,.Third series is3,10,17,24,See the least number in the third series which leaves remainder1on dividing by3and leaves remainder2on dividing by 5.⇒52is the least number of third series which leaves remainder1on dividing by3and leaves remainder2on dividing by5Now,A=52Dis L.C. M. of(3,5,7)=105⇒A+D=52+105=157.

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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

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