# Let AP (a;d) denote the set of all the terms of an infinite arithmetic progression with first term a and

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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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For common terms of 1st and 2nd series

For common terms of 2nd and 3rd series

⇒ First common term of 1st, 2nd and 3rd series (when n = 11)

a = 2 + (11 – 1)5 = 52

d = L.C.M. (3, 5, 7) = 105

⇒ a + d = 157.00