Let $\mathrm{AP}(a ; d)$ denote the set of all the terms of an infinite arithmetic progression with

Question

Let $\mathrm{AP}(a ; d)$ denote the set of all the terms of an infinite arithmetic progression with first term $a$ and common difference $d>0$. If $\operatorname{AP}(1 ; 3) \cap \operatorname{AP}(2 ; 5) \cap \operatorname{AP}(3 ; 7)=\operatorname{AP}(a ; d)$, then $a+d$ equals

Professor PC Thomas Classes · Answer

(157) : Let $1+3 m=2+5 n=3+7 r$ The first common term is given by putting $r=7$\ $	herefore \quad a=52$ and $d=$ least common multiple of $3,5,7=105$\ Hence, $a+d=105+52=157$\