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.

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

What is the product of the rational expressions below? 4x/x+6 /times x-8/x-6

Soloha48 [4]

Answer:

Step-by-step explanation:

Multiply the numerators together to get the overall numerator and multiply the denominators together to get the overall denominator. I hope this helps!