Question

If a,a+d,a+2d,...l is an AP then find the nth term from the end l.​

Answer 1

Answer:

nth term from the end = l - (n-1)d

Step-by-step explanation:

$given \ AP \ series, \\ a,a+d,a+2d,.......l \\\\ first \ term, a=a \\ common \ difference,d=(a+d)-a=(a+2d)-(a+d)=d\\last \ term,l=l \\\\ nth \ term \ of \ an \ AP \ is \ given \ by \\ a(n)=a+(n-1)d \ \ \ \ \ \ \ \ [from \ the \ starting ]\\\\Now,to \ find \ nth \ term \ of \ an \ AP \ from \ the \ end \\ reverse \ the \ series... \\\\ l,....a+2d,a+d,a \\\\here, first \ term=l\\common \ difference=a-(a+d)=-d\\last \ term = a \\\\ nth \ term \ from \ the \ end = a(n) = l+(n-1)(-d)\\a(n) =l-(n-1)d$