I suppose you mean
, and if we multiply
by
we get
. Subtracting this from the numerator gives a remainder of
.
, and multiplying
by
gives
. Subtracting this from the previous remainder gives a new remainder of
.
has no remaining factors of
in it, so we're done, and
The common ratio of both the formulas is 3 and 2. The first formula is explicit and the second is the recursive formula.
<h3>What is the recursive rule?</h3>A rule is defined such that its definition includes itself.
1.
The given sequence is
-2, -6, -18, -54
Common ratio ;
r = -6 / -2 = 3
This given formula is the explicit formula.
2.
The given sequence is
4, 8, 16, 32
Common ratio ;
r = 8 / 4 = 2
This given formula is the recursive formula.
Learn more about the recursive rule and explicit rules here:
#SPJ1
Look at the graph below carefully
Observe the results of shifting ={2}^{x}f(x)=2x
vertically:
The domain, (−∞,∞) remains unchanged.
When the function is shifted up 3 units to ={2}^{x}+3g(x)=2x +3:
The y-intercept shifts up 3 units to (0,4).
The asymptote shifts up 3 units to y=3y=3.
The range becomes (3,∞).
When the function is shifted down 3 units to ={2}^{x}-3h(x)=2 x −3:
The y-intercept shifts down 3 units to (0,−2).
The asymptote also shifts down 3 units to y=-3y=−3.
The range becomes (−3,∞).
