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:
Step-by-step explanation:
hello:
here an solution
Answer:
just use a calculator
Step-by-step explanation:
or use photo shop to get ez answers
Answer: 4
Step-by-step explanation:
Answer:
"The product of a rational number and an irrational number is SOMETIMES irrational." If you multiply any irrational number by the rational number zero, the result will be zero, which is rational. Any other situation, however, of a rational times an irrational will be irrational
A better statement would be:
"The product of a non-zero rational number and an irrational number is irrational
