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

1. ## 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

2. 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 ( $U_n - U_{n-1} = U_{n-1}-U_{n-2} =d$)

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

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

Geometric Sequence

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

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

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

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