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A geometric 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.

Examples

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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General Term

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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Sum of Terms

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)

8 0

3 years ago

Needing a answer ASAP! TYYY

dolphi86 [110]

Answer: 840 feet squared

Step-by-step explanation: 24ft * 35ft = 840

4 0

3 years ago

Read 2 more answers

SAVE ME. Please Answer my Questions Clevers.

Vladimir [108]

Answer:

See below

Step-by-step explanation:

Q1. if a counting number is selected at random from a set of whole number less than or equal to 20 find the probability of getting:

Counting numbers are Natural numbers: $\mathbb{N}$

Also, we have Whole numbers. Despite not having an official symbol, I usually denote the set as $\mathbb{Z}_{\ge 0}$

Whole numbers less than or equal to 20: $A\leq 20, A \subset \mathbb{Z}_{\ge 0} \\\implies A=\{0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20\}$