Explanation:
A sequence is a list of numbers.
A <em>geometric</em> sequence is a list of numbers such that the ratio of each number to the one before it is the same. The common ratio can be any non-zero value.
<u>Examples</u>
- 1, 2, 4, 8, ... common ratio is 2
- 27, 9, 3, 1, ... common ratio is 1/3
- 6, -24, 96, -384, ... common ratio is -4
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<u>General Term</u>
Terms of a sequence are numbered starting with 1. We sometimes use the symbol a(n) or an to refer to the n-th term. The general term of a geometric sequence, a(n), can be described by the formula ...
a(n) = a(1)×r^(n-1) . . . . . n-th term of a geometric sequence
where a(1) is the first term, and r is the common ratio. The above example sequences have the formulas ...
- a(n) = 2^(n -1)
- a(n) = 27×(1/3)^(n -1)
- a(n) = 6×(-4)^(n -1)
You can see that these formulas are exponential in nature.
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<u>Sum of Terms</u>
Another useful formula for geometric sequences is the formula for the sum of n terms.
S(n) = a(1)×(r^n -1)/(r -1) . . . . . sum of n terms of a geometric sequence
When |r| < 1, the sum converges as n approaches infinity. The infinite sum is ...
S = a(1)/(1-r)
Answer:
40 square inches.
Step-by-step explanation:
It is given that the new club sticker is in the shape of a triangle.
Height of triangle = 8 inches
Base of triangle = 10 inches
We need to find the area of sticker.
Area of triangle 
Substitute base = 10 and height = 8 in the above formula.
Area of triangle 
Area of triangle 
Area of triangle 
Therefore, the area of the club sticker is 40 square inches.
Answer:
Use the "find vertically opposite angle" method.
a = 80°
To find the other angles:
Since the angles equal up to 360 which makes a full circle shape...
360 - 80 - 80 = 200 (B and C)
200 ÷ 2 = 100 (Angle for B and C since they are vertically opposite, hence having the same angle)
b = 100°
c = 100°
Answer:
∠O = 95°
Step-by-step explanation:
since ∠Q = 85°, arc NOP = 2(85°) = 170°
arc PQN = 360° - arc NOP
arc PQN = 360° - 170° = 190°
∠O = 1/2(arc PQN) = 1/2(190°) = 95°
Use Pythagorean Theorem:
a² + b² = c²
"a" is one side of the right triangle.
Its length is: radius of larger circle minus radius of smaller circle: (11 - 3 = 8)
The distance between the center of the circles creates the hypotenuse (17)
8² + b² = 17²
b² = 225
b = 15
Answer: the length of the common external tangent is 15.
