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)
Given:
The frequency distribution table.
To find:
The mean average score on a test.
Solution:
The frequency distribution table is
x a xa
y b yb
z c zc
Sum a+b+c xa+yb+zc
Now, the mean average score on the test is
Therefore, the mean average score on the test is 
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Newton's Law of Cooling
Tf=Ts+(Ti-Ts)e^(-kt) where Tf is temp at time t, Ts is temp of surroundings, Ti is temp of object/fluid. So we need to find k first.
200=68+(210-68)e^(-10k)
132=142e^(-10k)
132/142=e^(-10k)
ln(132/142)=-10k
k=-ln(132/142)/10
k≈0.0073 so
T(t)=68+142e^(-0.0073t) so how long until it reaches 180°?
180=68+142e^(-0.0073t)
112=142e^(-0.0073t)
112/142=e^(-0.0073t)
ln(112/142)=-0.0073t
t= -ln(112/142)/(0.0073)
t≈32.51 minutes
First, let's convert all of these numbers to decimal form:
(This will make it much easier to compare.)
- 0.6, - 0.625, - 0.4117, - 0.72
Now we can list them from least to greatest!
-0.4117, - 0.6, -0.625, -0.72
And don't forget to convert the selective decimals that we converted earlier back into fractions!
Therefore, the final list would be:
- 7/17, - 0.6, - 5/8, - 0.72
Hope this helps!
Multiply all terms by 15
3x+3x= 10x+30
Combine like terms
6x=10x+30
Subtract 10x from both sides
-4x=30
Divide both sides by -4
x= -7.5
Final answer: -7.5
