ACT Math 4.2 Pre-Algebra
ACT Math: Pre-Algebra Drill 4, Problem 2. What is the fourth term in the series?
|Algebra||Sequences and Series|
|Foreign Language||Arabic Subtitled|
|Intermediate Algebra||Sequences and patterns|
|Product Type||ACT Math|
Ugh. This one is... ugly. But maybe it's
pretty on the inside. Let's think this one through.
In any question where we have both a fraction AND a square root sign, odds are good that
they are testing us on whether or not we realize that a square root is just the inside part
raised to the one half power.
That is, the square root of x here is the same as x to the one half.
So... now that we are all living in Exponentland...
We have a series of 4 terms... and term 1 here is x to the one half.
Now we raise the power to three-halves for the second term -- and we know -- hopefully
-- that if we are raising exponents to powers we just multiply the exponents...
...so in this case we multiply one half by three halves to get x to the three-fourths
as the second term.
Now do it again to get the 3rd term.
We have x to the three-fourths to the power 3 over 2, which is multiplied to get 3/4 times
three-halves, or 9/8.
Almost to the promised land... located conveniently between Exponentland and Frontierland...
Ok... we have x to the 9/8 to the three-halves, so we multiply 9 over 8 by 3 over 2 to get
27 over 16... or x to the 27/16ths... and the answer is E.
As in, "Exponentland."