Math Sequences and Summation Notation

repeated multiplying patterns

use exponents

repeated adding patterns

use multiplication

Arithmetic Sequence nth term(Explicit)

an = a1 + (n-1)d

Geometric Sequence nth term(Explicit)

an = (a1)(r^n-1)

Arithmetic Sequence Partial Sum

Sn = (n/2)(a1 + an)

Geometric Sequence Partial Sum

Sn = a1(1-r^n / 1-r)

Arithmetic sequence recursive formula

an = a_n-1+d

Geometric sequence recursive formula

an = a_n-1(r)

infinite sum arithmetic sequence

N/A

Infinite sum geometric sequence

Sn = a/(1-r) , |r|<1

Summation Notation

n on top = end
k= _ is where to start

ak is formula

nCr

(n)
(r )
n!/ r!(n-r)!

Binomial theorem: (a + b)^n

(n j ) (a^n-j)(b^j)