# recursion patterns, arithmetic/geometric equations, and sigma notations

• Nov 4th 2009, 12:58 PM
sodumb:(
recursion patterns, arithmetic/geometric equations, and sigma notations
Could a kind soul please be so kind to explain what exactly the variables in the equations of arithmetic/geometric sequences mean? I would understand it so much more if i knew what u (sub N) or a meant. I have no notes:) Furthermore I do not quite grasp the concept of the sigma notation for my teacher is insane. Feel free to delve into that:)

Thank you
• Nov 4th 2009, 01:14 PM
e^(i*pi)
Quote:

Originally Posted by sodumb:(
Could a kind soul please be so kind to explain what exactly the variables in the equations of arithmetic/geometric sequences mean? I would understand it so much more if i knew what u (sub N) or a meant. I have no notes:) Furthermore I do not quite grasp the concept of the sigma notation for my teacher is insane. Feel free to delve into that:)

Thank you

U_n = nth term of a sequence

U_1 = a = first terms of a sequence

n = number of terms in a sequence or a specific term

Arithmetic Sequences

d = common difference ($\displaystyle U_n - U_{n-1} = U_{n-1}-U_{n-2} =d$)

nth term: $\displaystyle U_n = a+(n-1)d$

Sum of n terms: $\displaystyle S_n=\frac{n}{2}(2a + (n-1)d)$

Geometric Sequence

r = common ratio ($\displaystyle \frac{U_n}{U_{n-1}} = \frac{U_{n-1}}{U_{n-2}} = r$)

nth term: $\displaystyle U_n = ar^{n-1}$

sum to n terms ($\displaystyle |r| \geq 1$): $\displaystyle S_n = \frac{a(1-r^n)}{r^n} = \frac{a(r^n-1)}{r^n}$

Sum to infinity ($\displaystyle |r| < 1$): $\displaystyle S_{\infty} = \frac{a}{1-r}$