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:
$6.4
Step-by-step explanation:
You just do 32 × .2 to give you the discount of 6.4
You multiple by .2 because 20% as a decimal is .2 ( you do 20% divided by 100 to give you .2)
The numbers to complete the pattern are 125, 216, 343.
The complete pattern is 1, 8, 27, 64, 125, 216, 343.
Hope this helps.
<u>Answer: </u>120
Since there is the 100 in the triangle, the other two sides in the triangle are equal to each other. So they are both 40
So 180 - 40 = 120
54 - 14 = 40
40/5 = 8
Each friend recieved 8 beads
