What are the next three terms in the pattern 2, 6, 18, 54, ...?
2 answers:
Answer:
OPTION B: 162, 486, 1458
Step-by-step explanation:
The given sequence is 2, 6, 18, 54, . . .
It is a geometric sequence and the common difference is 3.
The general form of a geometric sequence is: a, ar, ar², ar³, . . .
Here a = 2 and r = 3.
term of a Geometric progression is
.
Note that the fourth term is 54.
i.e.,
.
Similarly, .
Also, .
Hence, OPTION B is the answer.
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Answer:
A. (3,1)
B. g(x)=|x-3|+6
C. h(x)=-|x-3|-6
Step-by-step explanation:
A. To graph the absolute value function f(x) = |x - 3| + 1, first graph the parent absolute value function y=|x| and then translate it 3 units to the right and 1 unit up (see green graph in attached diagram). The vertex of the function f(x) is at point (3,1).
B. The function g(x) translates f(x) 5 units up, so its equation is
g(x)=f(x)+5
g(x)=|x-3|+1+5
g(x)=|x-3|+6
Blue graph in attached diagram.
C. The function h(x) reflects g(x) over the x-axis, so the equation of the function h(x) is
h(x)=-g(x)
h(x)=-(|x-3|+6)
h(x)=-|x-3|-6
Red graph in attached diagram.
