Let's start by first remembering what a "geometric sequence" is. A geometric sequence is a sequence of numbers that multiply by the same number each time. For example,
2, 4, 8, 16
is a geometric sequence since each number is multiplied by 2 from one to the next, but
2, 4, 6, 8
is NOT a geometric sequence. We are adding 2 each time, but not multiplying, so it doesn't count. We have to be multiplying to have a geometric sequence.
[A] Let's look at A, are we multiplying by the same thing?
6*3 = 18
18*3 = 54
54*3 = 162
162*3 = 486
Yes! We are multiplying by 3 each time. This is a geometric sequence!
[B] Are we multiplying by the same thing?
2*3/2 = 3
3*3/2 = 9/2 which is not 5.
NOPE
[C] Are we multiplying by the same thing?
2*5/2 = 5
5*5/2 = 25/2 which is not 8
NOPE
[D] Are we multiplying by the same thing?
-4*1/2 = -2
-2*1/2 = -1
-1*1/2 = -0.5
-0.5*1/2 = -0.25
-0.25*1/2 = -0.125
Yep, we are multiplying by 1/2 each time! This is a geometric sequence!
Answer:
130°
Step-by-step explanation:
Arc QPN is formed by angle QNT. Angle QNT is formed by an intersecting tangent and chord meaning arc QPN is two times the measure of angle QNT.
65° · 2 = 130°
Answer: 20.5 units
Step-by-step explanation:
P=Perimeter
JI=3-(-3)
JI=3+3
JI=6
IK=7-1
IK=6
JK=(6^2+6^2)^1/2 ==> Distance Formula
JK=(36+36)^1/2
JK=(2*36)^1/2
JK=6(2)^1/2
P=JI+IK+JK
P=6+6+6(2)^1/2
P=12+6(2)^1/2
P=20.485 units
P=20.5 units
Given:
The arithmetic sequence is:
10, 12, 14, 16, ...
To find:
The function that generates the given sequence if n is an integer.
Solution:
We have,
10, 12, 14, 16, ...
Here, the first term is 10 and the common difference is:
The nth term of an arithmetic sequence is:
Where, a is the first term, d is the common difference and 
.
Putting 
in the above formula, we get
Therefore, the function 
generates the sequence.
