+613 When the same constant is added to the numbers $60,$ $120,$ and $160,$ a three-term geometric sequence arises. What is the common ratio of the resulting sequence?
+1946 Not too bad of a problem!
Let's let n be the constant we add to the 3 numbers. Lets try to figure out the 3 new numbers first.
Since all terms form a geometric sequence, we can write
120+n60+n=160+n120+n(120+n)2=(60+n)(160+n)14400+n2+240n=9600+n2+220n4800=−20nn=−240
Now, I know the n is negative, when if we apply it, we dot get -180, -120, and -80, which do form a geometric series.
-180/-120 = 3/2, so 3/2 is the answer.
I'm not sure if this is the correct answer, but it does work.
Thanks! :)
