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)
The independent variable is hours and the score or points is the dependent variable .equation is s=3h
Answer:
The twins would be 13 years old.
Step-by-step explanation:
21+21+21+13+13 = 89
Solving for x you would get X=6
The answer is: 45 * 10 ⁻¹¹ .
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Explanation:
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Given: (9 * 10⁻⁵) * (5 *10 ⁻⁶) ; Simplify.
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(9 * 10⁻⁵) * (5 *10⁻⁶) =
9 * 5 * 10⁻⁵ * 10⁻⁶ =
(9 * 5) * 10⁻⁵ * 10⁻⁶
45 * 10⁻⁵ * 10⁻⁶ ;
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Note the following property of exponents:
xᵃ * xᵇ = x⁽ᵃ⁺ᵇ⁾ ;
As such, 10⁻⁵ * 10⁻⁶ = 10⁽⁻⁵ ⁺ ⁻⁶) = 10 ⁻¹¹ ;
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So; 45 * 10⁻⁵ * 10⁻⁶
= 45 * 10⁻¹¹ .
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