sequences and series

Arithmetic Sequence nth Term

a_n = a_1 + d(n-1)

Arithmetic Sequence Sum

S_n = ((a_1 + a_n)/2) * n

Common Difference

d = a_2 - a_1

Geometric Sequence nth Term

a_n = a_1 * r^(n-1)

Common Ratio

r = a_2 / a_1

Infinite Geometric Series Sum

S∞ = a_1 / (1 - r)

Sigma Notation (Arithmetic)

Σ from i=1 to n of (a_1 + (i-1)d)

Sigma Notation (Geometric)

Σ from i=1 to n of a_1 * r^(i-1)

Monthly Deposit Formula

A = P((1+r)^n - 1) / r

Monthly Deposit Variables

P = monthly deposit, r = monthly interest rate, n = number of deposits

Factorial

n! = n(n-1)(n-2)…(1)

Example Factorial

10! = 10·9·8·7·6·5·4·3·2·1

Percent Increase Formula

a_n = a_1(1 + p)^(n)

Percent Decrease Formula

a_n = a_1(1 - p)^(n)