Suppose the nth term is = arn where n = 1,2,3, ...
Then the sum to the nth term is a*(rn+1 - 1)/(r - 1) or, equivalently,
a*(1 - rn+1)/(1 - r)
A Postulate,
In a Geometric Sequence each term is found by multiplying the previous term by a common ratio except the first term and the general rule is ar^(n-1) whereas a is the first term, r is the common ratio and (n-1) is term number minus 1
the rule for chains of geometric shapes
The sum of the terms in a sequence is called a series. Sequence is a function whose domain is the natural numbers. So f(1)= first entry in the sequence, and f(2) is the next.... f(n) is the nth term. We usually don't write sequences that way. Instead of f(1) we write, a1 to refer to the first term. The function tells us the rule we use to find the terms of the sequence. So for example, f says take n and square it. Then the first 3 terms of the sequence are 1, 4 and 9 and the first 3 terms of the series are 1, 5 and 14
Each term is the sum of the two terms before it. That's the famous "Fibonacci" series.
A Postulate,
In a Geometric Sequence each term is found by multiplying the previous term by a common ratio except the first term and the general rule is ar^(n-1) whereas a is the first term, r is the common ratio and (n-1) is term number minus 1
the rule for chains of geometric shapes
The sum of the terms in a sequence is called a series. Sequence is a function whose domain is the natural numbers. So f(1)= first entry in the sequence, and f(2) is the next.... f(n) is the nth term. We usually don't write sequences that way. Instead of f(1) we write, a1 to refer to the first term. The function tells us the rule we use to find the terms of the sequence. So for example, f says take n and square it. Then the first 3 terms of the sequence are 1, 4 and 9 and the first 3 terms of the series are 1, 5 and 14
The first step is to find the sequence rule. The sequence could be arithmetic. quadratic, geometric, recursively defined or any one of many special sequences. The sequence rule will give you the value of the nth term in terms of its position, n. Then simply substitute the next value of n in the rule.
Each term is the sum of the two terms before it. That's the famous "Fibonacci" series.
n2+n
Mean of the growth of a population, investments, etc. Rule of thumb for geometric mean: THE FORMULA INVOLVES GROWTH, i.e. is exponential in nature.
The first rule of geometry..... do not talk about geometry. The second rule of geometry..... DO NOT TALK ABOUT GEOMETRY hahah But seriously you'll have to be a bit more specific here cos there's too many geometric rules to list!
Sn = n^2
I forget his name, but its something like Pythagoreus, as the rule is called the "Pythagorean Theorem"
It is the description of a rule which describes how the terms of a sequence are defined in terms of their position in the sequence.